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Homology Homotopy and Applications最新文献

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The structuring effect of a Gottlieb element on the Sullivan model of a space 戈特利布元素对空间沙利文模型的结构效应
4区 数学
Homology Homotopy and Applications Pub Date : 2023-01-01 DOI: 10.4310/hha.2023.v25.n2.a12
Gregory Lupton, Samuel Bruce Smith
{"title":"The structuring effect of a Gottlieb element on the Sullivan model of a space","authors":"Gregory Lupton, Samuel Bruce Smith","doi":"10.4310/hha.2023.v25.n2.a12","DOIUrl":"https://doi.org/10.4310/hha.2023.v25.n2.a12","url":null,"abstract":"We show a Gottlieb element in the rational homotopy of a simply connected space $X$ implies a structural result for the Sullivan minimal model, with different results depending on parity. In the even-degree case, we prove a rational Gottlieb element is a terminal homotopy element. This fact allows us to complete an argument of Dupont to prove an even-degree Gottlieb element gives a free factor in the rational cohomology of a formal space of finite type. We apply the odd-degree result to affirm a special case of the $2N$-conjecture on Gottlieb elements of a finite complex. We combine our results to make a contribution to the realization problem for the classifying space $Bmathrm{aut}_1(X)$. We prove a simply connected space $X$ satisfying $Bmathrm{aut}_1(X_{mathbb{Q}}) simeq S_{mathbb{Q}}^{2n}$ must have infinite-dimensional rational homotopy and vanishing rational Gottlieb elements above degree $2n-1$ for $n= 1, 2, 3.$","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135319886","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
Cyclic $A_infty$-algebras and cyclic homology 循环$A_infty$ -代数与循环同调
IF 0.5 4区 数学
Homology Homotopy and Applications Pub Date : 2023-01-01 DOI: 10.4310/hha.2023.v25.n1.a15
E. Herscovich
{"title":"Cyclic $A_infty$-algebras and cyclic homology","authors":"E. Herscovich","doi":"10.4310/hha.2023.v25.n1.a15","DOIUrl":"https://doi.org/10.4310/hha.2023.v25.n1.a15","url":null,"abstract":"","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70435124","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
Complex orientations and $mathrm{TP}$ of complete DVRs 完全dvr的复取向和$ mathm {TP}$
IF 0.5 4区 数学
Homology Homotopy and Applications Pub Date : 2023-01-01 DOI: 10.4310/hha.2023.v25.n1.a16
Gabriel Angelini-Knoll
{"title":"Complex orientations and $mathrm{TP}$ of complete DVRs","authors":"Gabriel Angelini-Knoll","doi":"10.4310/hha.2023.v25.n1.a16","DOIUrl":"https://doi.org/10.4310/hha.2023.v25.n1.a16","url":null,"abstract":"","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70435136","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 homotopy solvability of compact Lie groups and homogenous topological spaces 紧李群与齐次拓扑空间的同伦可解性
4区 数学
Homology Homotopy and Applications Pub Date : 2023-01-01 DOI: 10.4310/hha.2023.v25.n2.a5
Marek Golasiński
{"title":"The homotopy solvability of compact Lie groups and homogenous topological spaces","authors":"Marek Golasiński","doi":"10.4310/hha.2023.v25.n2.a5","DOIUrl":"https://doi.org/10.4310/hha.2023.v25.n2.a5","url":null,"abstract":"","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136004371","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
Stable equivariant complex cobordism of the symmetric group on three elements 三元对称群的稳定等变复协
IF 0.5 4区 数学
Homology Homotopy and Applications Pub Date : 2023-01-01 DOI: 10.4310/hha.2023.v25.n1.a5
P. Hu, I. Kríz, Yunzeng Lu
{"title":"Stable equivariant complex cobordism of the symmetric group on three elements","authors":"P. Hu, I. Kríz, Yunzeng Lu","doi":"10.4310/hha.2023.v25.n1.a5","DOIUrl":"https://doi.org/10.4310/hha.2023.v25.n1.a5","url":null,"abstract":"","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70435489","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 homology of connective Morava $E$-theory with coefficients in $mathbb{F}_p$ 的同源性连接摩拉瓦河与系数E理论美元美元 mathbb {F} _p美元
4区 数学
Homology Homotopy and Applications Pub Date : 2023-01-01 DOI: 10.4310/hha.2023.v25.n2.a8
Lukas Katthän, Sean Tilson
{"title":"The homology of connective Morava $E$-theory with coefficients in $mathbb{F}_p$","authors":"Lukas Katthän, Sean Tilson","doi":"10.4310/hha.2023.v25.n2.a8","DOIUrl":"https://doi.org/10.4310/hha.2023.v25.n2.a8","url":null,"abstract":"Let $e_n$ be the connective cover of the Morava $E$-theory spectrum $E_n$ of height $n$. In this paper we compute its homology $H_*(e_n;mathbb{F}_p)$ for any prime $p$ and $n leq 4$ up to possible multiplicative extensions. In order to accomplish this we show that the Kunneth spectral sequence based on an $E_3$-algebra $R$ is multiplicative when the $R$-modules in question are commutative $S$-algebras. We then apply this result by working over $BP$ which is known to be an $E_4$-algebra.","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135783615","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
When Bousfield localizations and homotopy idempotent functors meet again 当Bousfield局域化与同伦幂等函子再次相遇时
4区 数学
Homology Homotopy and Applications Pub Date : 2023-01-01 DOI: 10.4310/hha.2023.v25.n2.a9
Victor Carmona
{"title":"When Bousfield localizations and homotopy idempotent functors meet again","authors":"Victor Carmona","doi":"10.4310/hha.2023.v25.n2.a9","DOIUrl":"https://doi.org/10.4310/hha.2023.v25.n2.a9","url":null,"abstract":"We adopt semimodel categories to extend fundamental results related to Bousfield localizations of model categories. More specifically, we generalize Bousfield-Friedlander Theorem and Hirschhorn Localization Theorem of cellular model categories to settings where their classical formulation does not apply. We use such results to answer, in the world of semimodel categories, an open problem posed by May-Ponto about the existence of Bousfield localizations for Hurewicz and mixed type model structures.","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135319884","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: 2
The classifying space of the 1+1 dimensional $G$-cobordism category 1+1维$G$-协范畴的分类空间
4区 数学
Homology Homotopy and Applications Pub Date : 2023-01-01 DOI: 10.4310/hha.2023.v25.n2.a3
Carlos Segovia
{"title":"The classifying space of the 1+1 dimensional $G$-cobordism category","authors":"Carlos Segovia","doi":"10.4310/hha.2023.v25.n2.a3","DOIUrl":"https://doi.org/10.4310/hha.2023.v25.n2.a3","url":null,"abstract":"The 1+1 G-cobordism category, with G a finite group, is important in the construction of G-topological field theories which are completely determined by a G-Frobenius algebra. We give a description of the classifying space of this category generalizing the work of Ulrike Tillmann. Moreover, we compute the connected components and the fundamental group of this classifying space and we give a complete description of the classifying spaces of some important subcategories. Finally, we present some relations between the rank of the fundamental group of the G-cobordism category and the number of subgroups of the group G.","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135701253","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: 7
The homotopy-invariance of constructible sheaves 可构轴的同伦不变性
4区 数学
Homology Homotopy and Applications Pub Date : 2023-01-01 DOI: 10.4310/hha.2023.v25.n2.a6
Peter J. Haine, Mauro Porta, Jean-Baptiste Teyssier
{"title":"The homotopy-invariance of constructible sheaves","authors":"Peter J. Haine, Mauro Porta, Jean-Baptiste Teyssier","doi":"10.4310/hha.2023.v25.n2.a6","DOIUrl":"https://doi.org/10.4310/hha.2023.v25.n2.a6","url":null,"abstract":"The purpose of this paper is to explain why the functor that sends a stratified topological space $S$ to the $infty$-category of constructible (hyper)sheaves on $S$ with coefficients in a large class of presentable $infty$categories is homotopy-invariant. To do this, we first establish a number of results in the unstratified setting, i.e., the setting of locally constant (hyper)sheaves. For example, if $X$ is a locally weakly contractible topological space and $mathcal{E}$ is a presentable $infty$-category, then we give a concrete formula for the constant hypersheaf functor $mathcal{E}to mathrm{Sh}^{mathrm{hyp}}(X;mathcal{E})$. This formula lets us show that the constant hypersheaf functor is a right adjoint, and is fully faithful if $X$ is also weakly contractible. It also lets us prove a general monodromy equivalence and categorical K\"unneth formula for locally constant hypersheaves.","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136002590","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: 6
On invertible $2$-dimensional framed and $r$-spin topological field theories 可逆$2维框架和$r$自旋拓扑场论
4区 数学
Homology Homotopy and Applications Pub Date : 2023-01-01 DOI: 10.4310/hha.2023.v25.n1.a6
Lóránt Szegedy
{"title":"On invertible $2$-dimensional framed and $r$-spin topological field theories","authors":"Lóránt Szegedy","doi":"10.4310/hha.2023.v25.n1.a6","DOIUrl":"https://doi.org/10.4310/hha.2023.v25.n1.a6","url":null,"abstract":"We classify invertible 2-dimensional framed and $r$-spin topological field theories by computing the homotopy groups and the $k$-invariant of the corresponding bordism categories. By a recent result of Kreck, Stolz and Teichner the first homotopy groups are given by the so called SKK groups. We compute them explicitly using the combinatorial model of framed and $r$-spin surfaces of Novak, Runkel and the author.","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135783360","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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