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Journal of Homotopy and Related Structures最新文献

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The stable Picard group of (mathcal {A}(n)) 稳定的皮卡德群 (mathcal {A}(n))
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-10-24 DOI: 10.1007/s40062-025-00387-4
JianZhong Pan, RuJia Yan
{"title":"The stable Picard group of (mathcal {A}(n))","authors":"JianZhong Pan,&nbsp;RuJia Yan","doi":"10.1007/s40062-025-00387-4","DOIUrl":"10.1007/s40062-025-00387-4","url":null,"abstract":"<div><p>In this paper, we show that, for <span>(nge 2)</span>, the stable Picard group of <span>(mathcal {A}(n))</span> is <span>(mathbb {Z}oplus mathbb {Z})</span>, where <span>(mathcal {A}(n))</span> is the usual finite sub Hopf algebra of the Steenrod algebra <span>(mathcal {A})</span> at the prime 2. The proof relies on reductions from a Hopf algebra to certain sub Hopf algebras.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"21 1","pages":"23 - 43"},"PeriodicalIF":0.5,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341922","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
Cohomology at infinity and the well-tempered complex 无穷远上同调与均匀复形
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-10-18 DOI: 10.1007/s40062-025-00385-6
Dylan Galt, Mark McConnell
{"title":"Cohomology at infinity and the well-tempered complex","authors":"Dylan Galt,&nbsp;Mark McConnell","doi":"10.1007/s40062-025-00385-6","DOIUrl":"10.1007/s40062-025-00385-6","url":null,"abstract":"<div><p>We prove the existence of a sequence of commutative diagrams generalizing the results on cohomology at infinity described in Ash and McConnell (Duke Math J 90:549–576, 1997) to the context of the well-tempered complex introduced in McConnell and MacPherson (Computing Hecke operators for arithmetic subgroups of general linear groups, http://arxiv.org/abs/2010.06036, 2020). Our main theorem provides a method for computing in finite terms the action of Hecke operators on the cohomology of the Borel-Serre boundary for the <span>(text {SL} _n)</span> symmetric space.\u0000</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"21 1","pages":"1 - 21"},"PeriodicalIF":0.5,"publicationDate":"2025-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147339954","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
Morava K-theory rings for finite groups 有限群的Morava k -理论环
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-10-16 DOI: 10.1007/s40062-025-00384-7
Malkhaz Bakuradze
{"title":"Morava K-theory rings for finite groups","authors":"Malkhaz Bakuradze","doi":"10.1007/s40062-025-00384-7","DOIUrl":"10.1007/s40062-025-00384-7","url":null,"abstract":"<div><p>This paper compiles and expands upon the author’s and his co-authors’ explicit calculations of the mod <i>p</i> Morava K-theory for various finite <i>p</i>-groups, a body of work currently scattered across different publications. The primary focus is on the author’s observations regarding the properties of formal group laws and the transfer in Morava K-theory. Using specific examples, this work aims to clarify the complex issues surrounding the multiplicative structure and the representation of Gröbner bases in terms of Chern classes and their transfers. A key computational question remains: is the mod 2 Morava K-theory of any finite 2-group completely generated by Chern classes and their transfers? While this conjecture by Hopkins et al. (J Am Math Soc 13:553–594, 2000), inspired by their generalized character theory of finite <i>p</i>-groups, was disproven for the mod <span>(p&gt;2)</span> case by a counterexample in Kriz (Topology 36:1247–1273, 1997), the mod 2 case remains an open problem.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 4","pages":"567 - 630"},"PeriodicalIF":0.5,"publicationDate":"2025-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145429131","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
Revisiting the Nandakumar–Ramana Rao conjecture 重新审视Nandakumar-Ramana Rao猜想
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-09-09 DOI: 10.1007/s40062-025-00383-8
Surojit Ghosh, Ankit Kumar
{"title":"Revisiting the Nandakumar–Ramana Rao conjecture","authors":"Surojit Ghosh,&nbsp;Ankit Kumar","doi":"10.1007/s40062-025-00383-8","DOIUrl":"10.1007/s40062-025-00383-8","url":null,"abstract":"<div><p>We reprove the generalized Nandakumar–Ramana Rao conjecture for the prime case using representation ring-graded Bredon cohomology. Our approach relies solely on the <span>(RO(C_p))</span>-graded cohomology of configuration spaces, viewed as a module over the <span>(RO(C_p))</span>-graded Bredon cohomology of a point.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 4","pages":"555 - 565"},"PeriodicalIF":0.5,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145429110","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
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
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