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ℂℙ2-stable classification of 4-manifolds withfinite fundamental group 具有有限基群的4-流形的2-稳定分类
arXiv: Geometric Topology Pub Date : 2019-07-27 DOI: 10.2140/PJM.2021.310.355
Daniel Kasprowski, P. Teichner
{"title":"ℂℙ2-stable classification of 4-manifolds with\u0000finite fundamental group","authors":"Daniel Kasprowski, P. Teichner","doi":"10.2140/PJM.2021.310.355","DOIUrl":"https://doi.org/10.2140/PJM.2021.310.355","url":null,"abstract":"We show that two closed, connected $4$-manifolds with finite fundamental groups are $mathbb{CP}^2$-stably homeomorphic if and only if their quadratic $2$-types are stably isomorphic and their Kirby-Siebenmann invariant agrees.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"67 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82337953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Knots with Hopf crossing number at most one 结点的Hopf交叉数最多为1
arXiv: Geometric Topology Pub Date : 2019-07-26 DOI: 10.18910/75915
M. Mroczkowski
{"title":"Knots with Hopf crossing number at most one","authors":"M. Mroczkowski","doi":"10.18910/75915","DOIUrl":"https://doi.org/10.18910/75915","url":null,"abstract":"We consider diagrams of links in $S^2$ obtained by projection from $S^3$ with the Hopf map and the minimal crossing number for such diagrams. Knots admitting diagrams with at most one crossing are classified. Some properties of these knots are exhibited. In particular, we establish which of these knots are algebraic and, for such knots, give an answer to a problem posed by Fiedler.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81532770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Labels instead of coefficients: A label bracket ⋅ℒ which dominates the Jones polynomial 𝒳 ⋅, the Kuperberg bracket ⋅A2, and the normalized arrow polynomial 𝒲⋅ 标签代替系数:一个标签括号⋅￣，它支配着Jones多项式∈⋅⋅、Kuperberg括号⋅A2和归一化箭头多项式𝒲⋅
arXiv: Geometric Topology Pub Date : 2019-07-15 DOI: 10.1142/s0218216520400015
A. A. Akimova, V. Manturov
{"title":"Labels instead of coefficients: A label bracket ⋅ℒ which dominates the Jones polynomial 𝒳 ⋅, the Kuperberg bracket ⋅A2, and the normalized arrow polynomial 𝒲⋅","authors":"A. A. Akimova, V. Manturov","doi":"10.1142/s0218216520400015","DOIUrl":"https://doi.org/10.1142/s0218216520400015","url":null,"abstract":"In the present paper, we develop a picture formalism which gives rise to an invariant that dominates several known invariants of classical and virtual knots: the Jones polynomial, the Kuperberg bracket, and the normalised arrow polynomial.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72823846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Generalized Bott–Cattaneo–Rossi invariants of high-dimensional long knots 高维长节的广义bot - cattaneo - rossi不变量
arXiv: Geometric Topology Pub Date : 2019-07-03 DOI: 10.2969/JMSJ/82908290
David Leturcq
{"title":"Generalized Bott–Cattaneo–Rossi invariants of high-dimensional long knots","authors":"David Leturcq","doi":"10.2969/JMSJ/82908290","DOIUrl":"https://doi.org/10.2969/JMSJ/82908290","url":null,"abstract":"Bott, Cattaneo and Rossi defined invariants of long knots $mathbb R^n hookrightarrow mathbb R^{n+2}$ as combinations of configuration space integrals. Here, we give a more flexible definition of these invariants. Our definition allows us to interpret these invariants as counts of diagrams. It extends to long knots inside more general $(n+2)$-manifolds, called parallelized asymptotic homology $mathbb R^{n+2}$, and provides invariants of these knots.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85026123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Single-cylinder square-tiled surfaces and the ubiquity of ratio-optimising pseudo-Anosovs 单柱方形平铺表面和无处不在的比例优化伪anosov
arXiv: Geometric Topology Pub Date : 2019-06-05 DOI: 10.1090/TRAN/8374
Luke Jeffreys
{"title":"Single-cylinder square-tiled surfaces and the ubiquity of ratio-optimising pseudo-Anosovs","authors":"Luke Jeffreys","doi":"10.1090/TRAN/8374","DOIUrl":"https://doi.org/10.1090/TRAN/8374","url":null,"abstract":"In every connected component of every stratum of Abelian differentials, we construct square-tiled surfaces with one vertical and one horizontal cylinder. We show that for all but the hyperelliptic components this can be achieved in the minimum number of squares necessary for a square-tiled surface in that stratum. For the hyperelliptic components, we show that the number of squares required is strictly greater and construct surfaces realising these bounds. \u0000Using these surfaces, we demonstrate that pseudo-Anosov homeomorphisms optimising the ratio of Teichmuller to curve graph translation length are, in a reasonable sense, ubiquitous in the connected components of strata of Abelian differentials. Finally, we present a further application to filling pairs on punctured surfaces by constructing filling pairs whose algebraic and geometric intersection numbers are equal.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87829333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Periodic projections of alternating knots 交替结的周期性投影
arXiv: Geometric Topology Pub Date : 2019-05-31 DOI: 10.1016/J.TOPOL.2021.107753
Antonio F. Costa, Cam Van Quach-Hongler
{"title":"Periodic projections of alternating knots","authors":"Antonio F. Costa, Cam Van Quach-Hongler","doi":"10.1016/J.TOPOL.2021.107753","DOIUrl":"https://doi.org/10.1016/J.TOPOL.2021.107753","url":null,"abstract":"","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84158350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Higher arity self-distributive operations in Cascades and their cohomology 级联中的高密度自分布运算及其上同调
arXiv: Geometric Topology Pub Date : 2019-05-01 DOI: 10.1142/s0219498821501164
M. Elhamdadi, M. Saito, E. Zappala
{"title":"Higher arity self-distributive operations in Cascades and their cohomology","authors":"M. Elhamdadi, M. Saito, E. Zappala","doi":"10.1142/s0219498821501164","DOIUrl":"https://doi.org/10.1142/s0219498821501164","url":null,"abstract":"We investigate constructions of higher arity self-distributive operations, and give relations between cohomology groups corresponding to operations of different arities. For this purpose we introduce the notion of mutually distributive $n$-ary operations generalizing those for the binary case, and define a cohomology theory labeled by these operations. A geometric interpretation in terms of framed links is described, with the scope of providing algebraic background of constructing $2$-cocycles for framed link invariants. This theory is also studied in the context of symmetric monoidal categories. Examples from Lie algebras, coalgebras and Hopf algebras are given.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"145 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86211391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
A note on the orderability of Dehn fillings of the manifold v2503 关于流形v2503的Dehn填充的有序性的注记
arXiv: Geometric Topology Pub Date : 2019-04-16 DOI: 10.1142/s0218216520710029
K. Varvarezos
{"title":"A note on the orderability of Dehn fillings of the manifold v2503","authors":"K. Varvarezos","doi":"10.1142/s0218216520710029","DOIUrl":"https://doi.org/10.1142/s0218216520710029","url":null,"abstract":"We show that Dehn filling on the manifold $v2503$ results in a non-orderable space for all rational slopes in the interval $(-infty , -1)$. This is consistent with the L-space conjecture, which predicts that all fillings will result in a non-orderable space for this manifold.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78213845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Small eigenvalues of random 3-manifolds 随机3流形的小特征值
arXiv: Geometric Topology Pub Date : 2019-03-19 DOI: 10.1090/tran/8564
U. Hamenstaedt, Gabriele Viaggi
{"title":"Small eigenvalues of random 3-manifolds","authors":"U. Hamenstaedt, Gabriele Viaggi","doi":"10.1090/tran/8564","DOIUrl":"https://doi.org/10.1090/tran/8564","url":null,"abstract":"We show that for every $ggeq 2$ there exists a number $c=c(g)>0$ such that the smallest positive eigenvalue of a random closed 3-manifold $M$ of Heegaard genus $g$ is at most $c(g)/{rm vol}(M)^2$.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"93 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80261510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Directed diagrammatic reducibility 有向图可约性
arXiv: Geometric Topology Pub Date : 2019-03-11 DOI: 10.1016/j.topol.2020.107307
J. Harlander, Stephan Rosebrock
{"title":"Directed diagrammatic reducibility","authors":"J. Harlander, Stephan Rosebrock","doi":"10.1016/j.topol.2020.107307","DOIUrl":"https://doi.org/10.1016/j.topol.2020.107307","url":null,"abstract":"","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90997635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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