数学最新文献

{"title":"Groups with exotic finiteness properties from complex Morse theory","authors":"Claudio Llosa Isenrich,&nbsp;Pierre Py","doi":"10.1112/topo.70013","DOIUrl":"https://doi.org/10.1112/topo.70013","url":null,"abstract":"<p>Recent constructions have shown that interesting behaviours can be observed in the finiteness properties of Kähler groups and their subgroups. In this work, we push this further and exhibit, for each integer <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>, new hyperbolic groups admitting surjective homomorphisms to <span></span><math>\u0000 <semantics>\u0000 <mi>Z</mi>\u0000 <annotation>${mathbb {Z}}$</annotation>\u0000 </semantics></math> and to <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>Z</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>${mathbb {Z}}^{2}$</annotation>\u0000 </semantics></math>, whose kernel is of type <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>k</mi>\u0000 </msub>\u0000 <annotation>$mathcal {F}_{k}$</annotation>\u0000 </semantics></math> but not of type <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$mathcal {F}_{k+1}$</annotation>\u0000 </semantics></math>. By a fibre product construction, we also find examples of non-normal subgroups of Kähler groups with exotic finiteness properties.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"18 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Experience-driven learning and interactive rules under link weight adjustment promote cooperation in spatial prisoner's dilemma game","authors":"Shounan Lu ,&nbsp;Yang Wang","doi":"10.1016/j.amc.2025.129381","DOIUrl":"10.1016/j.amc.2025.129381","url":null,"abstract":"<div><div>Drawing on social learning theory, which emphasizes the dual influence of direct and indirect experience on behavior, this study extends the Spatial Prisoner's Dilemma game framework through three key innovations. First, we develop a link weight adjustment mechanism that incorporates tolerance, a previously neglected factor. Second, we extend the interaction probability model by integrating both direct and indirect link weights. Third, we design a strategy update rule where behavioral adaptation depends on combined experience learning. Simulation results show that our approach significantly outperforms traditional models in promoting cooperation. In particular, we identify an inverse relationship between tolerance and cooperation levels, with reduced defection sensitivity effectively protecting cooperators from exploitation. Furthermore, indirect experiences prove more powerful than direct interactions in sustaining cooperation. Together, these mechanisms increase cooperators' payoffs and competitive advantage. Integrating both direct and indirect experiences into policy updates offers a more comprehensive approach to addressing complex social challenges, as it enables decision-makers to leverage both personal insights and collective wisdom for more effective solutions.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"497 ","pages":"Article 129381"},"PeriodicalIF":3.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A heuristic algorithm for rainbow matchings and its application in rainbow Ramsey number for matchings","authors":"Zemin Jin","doi":"10.1016/j.dam.2025.02.040","DOIUrl":"10.1016/j.dam.2025.02.040","url":null,"abstract":"<div><div>It is well known that a maximum matching in a given graph can be found in polynomial time. The maximum rainbow matching problem is to find a rainbow matching of maximum size in an edge-colored graph. This problem is equivalent to the multiple choice matching problem which is <span><math><mrow><mi>N</mi><mi>P</mi></mrow></math></span>-Complete. Moreover, it is surprising that the rainbow matching problem is even <span><math><mrow><mi>A</mi><mi>P</mi><mi>X</mi></mrow></math></span>-Complete for paths. So far, there is few efficient algorithm for rainbow matchings. The only positive result is to reduce it to the maximum independent sets in <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></math></span>-free graphs, which can be approximated by a polynomial algorithm with approximation ratio <span><math><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mo>−</mo><mi>ϵ</mi></mrow></math></span> for every <span><math><mrow><mi>ϵ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. In this paper, we give a heuristic polynomial algorithm to find a large rainbow matching in an edge-colored <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. For any given integer <span><math><mi>k</mi></math></span>, we can find either a rainbow <span><math><mrow><mi>k</mi><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>, or a <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>3</mn><mi>i</mi></mrow></msub></math></span> with at most <span><math><mrow><mi>k</mi><mo>−</mo><mi>i</mi><mo>−</mo><mn>1</mn></mrow></math></span> colors for some <span><math><mrow><mn>0</mn><mo>≤</mo><mi>i</mi><mo>≤</mo><mi>k</mi><mo>−</mo><mn>2</mn></mrow></math></span>. It is interesting that our result is useful for the existence of a monochromatic <span><math><mi>G</mi></math></span> against a rainbow matching in <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. We give applications of the algorithm and, based on it, we generalize the previous results about the rainbow Ramsey number for matchings.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"368 ","pages":"Pages 153-161"},"PeriodicalIF":1.0,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143512581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the slice spectral sequence for quotients of norms of Real bordism","authors":"Agnès Beaudry,&nbsp;Michael A. Hill,&nbsp;Tyler Lawson,&nbsp;XiaoLin Danny Shi,&nbsp;Mingcong Zeng","doi":"10.1112/topo.70015","DOIUrl":"https://doi.org/10.1112/topo.70015","url":null,"abstract":"&lt;p&gt;In this paper, we investigate equivariant quotients of the Real bordism spectrum's multiplicative norm &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;U&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$MU^{(!(C_{2^n})!)}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; by permutation summands. These quotients are of interest because of their close relationship with higher real &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;annotation&gt;$K$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-theories. We introduce new techniques for computing the equivariant homotopy groups of such quotients. As a new example, we examine the theories &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;⟨&lt;/mo&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;mo&gt;⟩&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$BP^{(!(C_{2^n})!)}langle m,mrangle$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. These spectra serve as natural equivariant generalizations of connective integral Morava &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;annotation&gt;$K$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-theories. We provide a complete computation of the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;/msub","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"18 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weak Solutions and Simulations for a Generalized Phase-Field Crystal Model With Neumann Boundary Conditions","authors":"Guomei Zhao,&nbsp;Fan Wu,&nbsp;Peicheng Zhu","doi":"10.1111/sapm.70031","DOIUrl":"https://doi.org/10.1111/sapm.70031","url":null,"abstract":"<div>\u0000 \u0000 <p>We study a generalized phase-field crystal (GPFC) model, which is a quasilinear parabolic equation of sixth-order for an order parameter. The model is used to simulate the microstructure evolution in crystal growth, specifically focusing on the competition between square, hexagonal, and roll forms. Here, the global existence and uniqueness of weak solutions in three space dimensions are proved under Neumann boundary conditions by employing the Galerkin method. The rigorous connection between weak solutions to the PFC and the GPFC equations is established through an analysis of the asymptotic limit. Moreover, we carry out numerical simulations to validate the model.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bistable traveling waves of a nonlocal reaction–diffusion model with non-monotone birth pulse","authors":"Binxiang Dai,&nbsp;Yaobin Tang","doi":"10.1016/j.aml.2025.109519","DOIUrl":"10.1016/j.aml.2025.109519","url":null,"abstract":"<div><div>This paper considers a nonlocal reaction–diffusion model with a non-monotone birth pulse and a bistable response term. We define two monotone semiflows and, using the comparison argument, obtain the threshold dynamics between persistence and extinction in bounded domain. Moreover, we apply the asymptotic fixed point theorem to show the existence of bistable traveling wave solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109519"},"PeriodicalIF":2.9,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143520749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Superspace coinvariants and hyperplane arrangements","authors":"Robert Angarone ,&nbsp;Patricia Commins ,&nbsp;Trevor Karn ,&nbsp;Satoshi Murai ,&nbsp;Brendon Rhoades","doi":"10.1016/j.aim.2025.110185","DOIUrl":"10.1016/j.aim.2025.110185","url":null,"abstract":"<div><div>Let Ω be the <em>superspace ring</em> of polynomial-valued differential forms on affine <em>n</em>-space. The natural action of the symmetric group <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> on <em>n</em>-space induces an action of <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> on Ω. The <em>superspace coinvariant ring</em> is the quotient <em>SR</em> of Ω by the ideal generated by <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>-invariants with vanishing constant term. We give the first explicit basis of <em>SR</em>, proving a conjecture of Sagan and Swanson. Our techniques use the theory of hyperplane arrangements. We relate <em>SR</em> to instances of the Solomon–Terao algebras of Abe–Maeno–Murai–Numata and use exact sequences relating the derivation modules of certain ‘southwest closed’ arrangements to obtain the desired basis of <em>SR</em>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110185"},"PeriodicalIF":1.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Revealing consistent patterns and intrinsic mechanisms of subway systems via relative influence","authors":"Ting Yu ,&nbsp;Liang Gao ,&nbsp;Chaoyang Zhang ,&nbsp;Shixin Chang ,&nbsp;Xiao Han ,&nbsp;Bingfeng Si ,&nbsp;Jose F.F. Mendes","doi":"10.1016/j.chaos.2025.116186","DOIUrl":"10.1016/j.chaos.2025.116186","url":null,"abstract":"<div><div>Subway systems play a vital role in facilitating mobility within cities. However, the complex, nonlinear interactions between subway stations are difficult to capture using traditional approaches, which typically focus on static network structures or absolute passenger flow. These methods fail to adequately address the dynamic nature of subway systems and hinder cross-city comparisons. In this study, we integrate perspectives from dynamics and system science to quantify the relative influence between subway stations, accounting for both network connectivity and dynamic characteristics. This approach effectively eliminates biases related to city scale, allowing for meaningful cross-city comparisons. Additionally, we develop a simulation model that links individual travel behavior with collective-level phenomena, shedding light on the intrinsic mechanisms governing passenger flow. By analyzing relative influence, we define a station importance metric that reveals the functional roles of stations within the network. Empirical analyses of subway systems in Beijing, Chongqing, Nanjing, and Suzhou demonstrate consistent patterns in relative influence distributions across cities and time periods. These patterns align with a time-based, two-step preferential attachment mechanism governing passenger travel. A comparison of our proposed station importance metric with traditional centrality measures further validates its effectiveness. This research provides valuable insights into subway network operations, contributing to the optimization of system resilience and management strategies.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116186"},"PeriodicalIF":5.3,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quadratic solitons in higher-order topological insulators","authors":"Yaroslav V. Kartashov","doi":"10.1016/j.chaos.2025.116199","DOIUrl":"10.1016/j.chaos.2025.116199","url":null,"abstract":"<div><div>I consider higher-order topological insulator (HOTI) created in <span><math><msup><mi>χ</mi><mfenced><mn>2</mn></mfenced></msup></math></span> nonlinear medium and based on two-dimensional generalization of the Su-Schrieffer-Heeger waveguide array, where transition between trivial and topological phases is achieved by shift of the four waveguides in the unit cell towards its center or towards its periphery. Such HOTI can support linear topological corner states that give rise to rich families of quadratic topological solitons bifurcating from linear corner states. The presence of phase mismatch between parametrically interacting fundamental-frequency (FF) and second-harmonic (SH) waves drastically affects the bifurcation scenarios and domains of soliton existence, making the families of corner solitons much richer in comparison with those in HOTIs with cubic nonlinearity. For instance, the internal soliton structure strongly depends on the location of propagation constant in forbidden gaps in spectra of <em>both</em> FF and SH waves. Two different types of corner solitons are obtained, where either FF or SH wave dominates in the bifurcation point from linear corner state. Because the waveguides are two-mode for SH wave, its spectrum features two groups of forbidden gaps with corner states of different symmetry appearing in each of them. Such corner states give rise to different families of corner solitons. Stability analysis shows that corner solitons in quadratic HOTI may feature wide stability domains and therefore are observable experimentally. These results illustrate how parametric nonlinear interactions enrich the behavior of topological excitations and allow to control their shapes.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116199"},"PeriodicalIF":5.3,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Kauffman bracket skein modules of small 3-manifolds","authors":"Renaud Detcherry ,&nbsp;Efstratia Kalfagianni ,&nbsp;Adam S. Sikora","doi":"10.1016/j.aim.2025.110169","DOIUrl":"10.1016/j.aim.2025.110169","url":null,"abstract":"<div><div>The proof of Witten's finiteness conjecture established that the Kauffman bracket skein modules of closed 3-manifolds are finitely generated over <span><math><mi>Q</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span>. In this paper, we develop a novel method for computing these skein modules.</div><div>We show that if the skein module <span><math><mi>S</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>Q</mi><mo>[</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>±</mo><mn>1</mn></mrow></msup><mo>]</mo><mo>)</mo></math></span> of <em>M</em> is tame (e.g. finitely generated over <span><math><mi>Q</mi><mo>[</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>±</mo><mn>1</mn></mrow></msup><mo>]</mo></math></span>), and the <span><math><mi>S</mi><mi>L</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>C</mi><mo>)</mo></math></span>-character scheme is reduced, then the dimension <span><math><msub><mrow><mi>dim</mi></mrow><mrow><mi>Q</mi><mo>(</mo><mi>A</mi><mo>)</mo></mrow></msub><mo>⁡</mo><mspace></mspace><mi>S</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>Q</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>)</mo></math></span> is the number of closed points in this character scheme. This, in particular, verifies a conjecture in the literature relating <span><math><msub><mrow><mi>dim</mi></mrow><mrow><mi>Q</mi><mo>(</mo><mi>A</mi><mo>)</mo></mrow></msub><mo>⁡</mo><mspace></mspace><mi>S</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>Q</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>)</mo></math></span> to the Abouzaid-Manolescu <span><math><mi>S</mi><mi>L</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>C</mi><mo>)</mo></math></span>-Floer theoretic invariants, for infinite families of 3-manifolds.</div><div>We prove a criterion for reducedness of character varieties of closed 3-manifolds and use it to compute the skein modules of Dehn fillings of <span><math><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-torus knots and of the figure-eight knot. The later family gives the first instance of computations of skein modules for closed hyperbolic 3-manifolds.</div><div>We also prove that the skein modules of rational homology spheres have dimension at least 1 over <span><math><mi>Q</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110169"},"PeriodicalIF":1.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}