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Journal of Homotopy and Related Structures最新文献

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On two quotients of (S^2times S^2) 的两个商 (S^2times S^2)
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-09-03 DOI: 10.1007/s40062-025-00382-9
Andrea Bianchi
{"title":"On two quotients of (S^2times S^2)","authors":"Andrea Bianchi","doi":"10.1007/s40062-025-00382-9","DOIUrl":"10.1007/s40062-025-00382-9","url":null,"abstract":"<div><p>In this note we prove that two seemingly different smooth 4-manifolds arising as quotients of <span>(S^2times S^2)</span> by free actions of <span>(mathbb {Z}/4)</span> are in fact diffeomorphic, answering a question of Hambleton and Hillman.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 4","pages":"549 - 553"},"PeriodicalIF":0.5,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145429112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The connective KO-theory of the Eilenberg–MacLane space (K({mathbb Z}_2,2)), I: the (E_2) page Eilenberg-MacLane空间的关联ko理论(K({mathbb Z}_2,2)), 1: (E_2)页
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-08-28 DOI: 10.1007/s40062-025-00379-4
Donald M. Davis, W. Stephen Wilson
{"title":"The connective KO-theory of the Eilenberg–MacLane space (K({mathbb Z}_2,2)), I: the (E_2) page","authors":"Donald M. Davis,&nbsp;W. Stephen Wilson","doi":"10.1007/s40062-025-00379-4","DOIUrl":"10.1007/s40062-025-00379-4","url":null,"abstract":"<div><p>We compute the <span>(E_2)</span> page of the Adams spectral sequence converging to the connective <i>KO</i>-theory of the second mod 2 Eilenberg–MacLane space, <span>(ko_*(K({mathbb Z}_2,2)))</span>, where <span>({mathbb Z}_2)</span> is the cyclic group of order 2. This required a careful analysis of the structure of <span>(H^*(K({mathbb Z}_2,2);{mathbb Z}_2))</span> as a module over the subalgebra of the Steenrod algebra generated by <span>(operatorname {Sq}^1)</span> and <span>(operatorname {Sq}^2)</span>. Complete analysis of the spectral sequence is performed in [8].</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 4","pages":"511 - 521"},"PeriodicalIF":0.5,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-025-00379-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145429109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Endomorphisms of equivariant algebraic K-theory 等变代数k理论的自同态
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-08-26 DOI: 10.1007/s40062-025-00380-x
K. Arun Kumar, Girja S. Tripathi
{"title":"Endomorphisms of equivariant algebraic K-theory","authors":"K. Arun Kumar,&nbsp;Girja S. Tripathi","doi":"10.1007/s40062-025-00380-x","DOIUrl":"10.1007/s40062-025-00380-x","url":null,"abstract":"<div><p>We prove that for the action of a finite constant group scheme, equivariant algebraic <i>K</i>-theory is represented by a colimit of Grassmannians in the equivariant motivic homotopy category. Using this result we show that the set of endomorphisms of the equivariant motivic space defined by <span>(K_0(G,-))</span> coincides with the set of endomorphisms of infinite Grassmannians in the equivariant motivic homotopy category by explicitly computing the equivariant <i>K</i>-theory of Grassmannians.\u0000</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 4","pages":"523 - 547"},"PeriodicalIF":0.5,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145429111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A contramodule generalization of Neeman’s flat and projective module theorem Neeman平模定理和射影模定理的控制模推广
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-07-17 DOI: 10.1007/s40062-025-00378-5
Leonid Positselski
{"title":"A contramodule generalization of Neeman’s flat and projective module theorem","authors":"Leonid Positselski","doi":"10.1007/s40062-025-00378-5","DOIUrl":"10.1007/s40062-025-00378-5","url":null,"abstract":"<div><p>This paper builds on top of Positselski (J Homot Relat Struct 19(4):635–678, 2024). We consider a complete, separated topological ring <span>({mathfrak {R}})</span> with a countable base of neighborhoods of zero consisting of open two-sided ideals. The main result is that the homotopy category of projective left <span>({mathfrak {R}})</span>-contramodules is equivalent to the derived category of the exact category of flat left <span>({mathfrak {R}})</span>-contramodules, and also to the homotopy category of flat cotorsion left <span>({mathfrak {R}})</span>-contramodules. In other words, a complex of flat <span>({mathfrak {R}})</span>-contramodules is contraacyclic (in the sense of Becker) if and only if it is an acyclic complex with flat <span>({mathfrak {R}})</span>-contramodules of cocycles, and if and only if it is coacyclic as a complex in the exact category of flat <span>({mathfrak {R}})</span>-contramodules. These are contramodule generalizations of theorems of Neeman and of Bazzoni, Cortés–Izurdiaga, and Estrada.\u0000</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 4","pages":"477 - 510"},"PeriodicalIF":0.5,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145429113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Realization of saturated transfer systems on cyclic groups of order (p^nq^m) by linear isometries (N_infty )-operads 用线性等距(N_infty ) -算子实现(p^nq^m)阶循环群上的饱和传递系统
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-07-12 DOI: 10.1007/s40062-025-00377-6
Julie Bannwart
{"title":"Realization of saturated transfer systems on cyclic groups of order (p^nq^m) by linear isometries (N_infty )-operads","authors":"Julie Bannwart","doi":"10.1007/s40062-025-00377-6","DOIUrl":"10.1007/s40062-025-00377-6","url":null,"abstract":"<div><p>We prove a specific case of Rubin’s saturation conjecture about the realization of <i>G</i>-transfer systems, for <i>G</i> a finite cyclic group, by linear isometries <span>(N_infty )</span>-operads, namely the case of cyclic groups of order <span>(p^nq^m)</span> for <i>p</i>, <i>q</i> distinct primes and <span>(n,min mathbb {N})</span>.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 3","pages":"455 - 475"},"PeriodicalIF":0.5,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-025-00377-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Explicit sharbly cycles at the virtual cohomological dimension for (textrm{SL}_n(mathbb {Z})) 的虚上同调维上的显式锐循环 (textrm{SL}_n(mathbb {Z}))
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-07-09 DOI: 10.1007/s40062-025-00374-9
Avner Ash, Paul E. Gunnells, Mark McConnell
{"title":"Explicit sharbly cycles at the virtual cohomological dimension for (textrm{SL}_n(mathbb {Z}))","authors":"Avner Ash,&nbsp;Paul E. Gunnells,&nbsp;Mark McConnell","doi":"10.1007/s40062-025-00374-9","DOIUrl":"10.1007/s40062-025-00374-9","url":null,"abstract":"<div><p>Denote the virtual cohomological dimension of <span>(textrm{SL}_n(mathbb {Z}))</span> by <span>(t=n(n-1)/2)</span>. Let <i>St</i> denote the Steinberg module of <span>(textrm{SL}_n(mathbb {Q}))</span> tensored with <span>(mathbb {Q})</span>. Let <span>(Sh_bullet rightarrow St)</span> denote the sharbly resolution of the Steinberg module. By Borel–Serre duality, the one-dimensional <span>(mathbb {Q})</span>-vector space <span>(H^0(textrm{SL}_n(mathbb {Z}), mathbb {Q}))</span> is isomorphic to <span>(H_t(textrm{SL}_n(mathbb {Z}),St))</span>. We find an explicit generator of <span>(H_t(textrm{SL}_n(mathbb {Z}),St))</span> in terms of sharbly cycles and cosharbly cocycles. These methods may extend to other degrees of cohomology of <span>(textrm{SL}_n(mathbb {Z}))</span>.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 3","pages":"391 - 416"},"PeriodicalIF":0.5,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Higher (equivariant) topological complexity of Milnor manifolds 米尔诺流形的高（等变）拓扑复杂性
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-07-01 DOI: 10.1007/s40062-025-00376-7
Navnath Daundkar, Bittu Singh
{"title":"Higher (equivariant) topological complexity of Milnor manifolds","authors":"Navnath Daundkar,&nbsp;Bittu Singh","doi":"10.1007/s40062-025-00376-7","DOIUrl":"10.1007/s40062-025-00376-7","url":null,"abstract":"<div><p>J. Milnor introduced a specific class of codimension-1 submanifolds in the product of projective spaces, known as Milnor manifolds. This paper establishes precise bounds on the higher topological complexity of these manifolds and provides exact values for this invariant for numerous Milnor manifolds. Furthermore, we improve the upper bounds on the higher equivariant topological complexity. As an application, we obtain sharper bounds on the higher equivariant topological complexity of Milnor manifolds with free <span>(mathbb {Z}_2)</span> and <span>(S^1)</span>-actions.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 3","pages":"437 - 453"},"PeriodicalIF":0.5,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bigraded Poincaré polynomials and the equivariant cohomology of Rep((C_2))-complexes Rep ((C_2)) -配合物的重阶poincarcars多项式和等变上同调
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-06-27 DOI: 10.1007/s40062-025-00375-8
Eric Hogle
{"title":"Bigraded Poincaré polynomials and the equivariant cohomology of Rep((C_2))-complexes","authors":"Eric Hogle","doi":"10.1007/s40062-025-00375-8","DOIUrl":"10.1007/s40062-025-00375-8","url":null,"abstract":"<div><p>We are interested in computing the Bredon cohomology with coefficients in the constant Mackey functor <span>(underline{{mathbb {F}}_2})</span> for equivariant <span>(text {Rep}(C_2))</span> spaces, in particular for Grassmannian manifolds of the form <span>(operatorname {Gr}_k(V))</span> where <i>V</i> is some real representation of <span>(C_2.)</span> It is possible to create multiple distinct <span>(text {Rep}(C_2))</span> constructions of (and hence multiple filtration spectral sequences for) a given Grassmannian. For sufficiently small examples one may exhaustively compute all possible outcomes of each spectral sequence and determine if there exists a unique common answer. However, the complexity of such a computation quickly balloons in time and memory requirements. We introduce a statistic on <span>(mathbb {M}_2)</span>-modules valued in the polynomial ring <span>(mathbb Z[x,y])</span> which makes cohomology computation of Rep<span>((C_2))</span>-complexes more tractable, and we present some new results for Grassmannians.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 3","pages":"417 - 435"},"PeriodicalIF":0.5,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cosimplicial structure on pointed multiplicative operads 点乘法操作数上的共简结构
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-06-17 DOI: 10.1007/s40062-025-00372-x
V. Jacky III Batkam Mbatchou, Calvin Tcheka
{"title":"Cosimplicial structure on pointed multiplicative operads","authors":"V. Jacky III Batkam Mbatchou,&nbsp;Calvin Tcheka","doi":"10.1007/s40062-025-00372-x","DOIUrl":"10.1007/s40062-025-00372-x","url":null,"abstract":"<div><p>Motivated by the work of Gerstenhaber-Voronov and that of Malvenuto-Reuternauer, we define on pointed multiplicative operads in the category of vector spaces over an arbitrary ground field <span>(mathbb {K})</span>, a cosimplicial vector space structure. This permits us to construct on such operads some algebraic structures such as the homotopy G-algebra and the bicomplex algebra structures. Moreover we illustrate our constructions through some examples and explain or extend some well-known results.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 3","pages":"365 - 385"},"PeriodicalIF":0.5,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Concerning monoid structures on naive homotopy classes of endomorphisms of punctured affine space 刺穿仿射空间中自同态的朴素同伦类上的单群结构
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-06-16 DOI: 10.1007/s40062-025-00373-w
Thomas Brazelton, William Hornslien
{"title":"Concerning monoid structures on naive homotopy classes of endomorphisms of punctured affine space","authors":"Thomas Brazelton,&nbsp;William Hornslien","doi":"10.1007/s40062-025-00373-w","DOIUrl":"10.1007/s40062-025-00373-w","url":null,"abstract":"<div><p>Cazanave proved that the set of naive <span>(mathbb {A}^1)</span>-homotopy classes of endomorphisms of the projective line admits a monoid structure whose group completion is genuine <span>(mathbb {A}^1)</span>-homotopy classes of endomorphisms of the projective line. In this very short note we show that, over a field which is not quadratically closed, such a statement is never true for punctured affine space <span>(mathbb {A}^nhspace{-0.1em}smallsetminus {0})</span> for <span>(nge 2)</span>.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 3","pages":"387 - 390"},"PeriodicalIF":0.5,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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