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Homology Homotopy and Applications最新文献

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An $R$-motivic v1-self-map of periodicity $1$ 周期$1$的$R$动机v1-自映射
IF 0.5 4区 数学
Homology Homotopy and Applications Pub Date : 2022-01-01 DOI: 10.4310/hha.2022.v24.n1.a15
P. Bhattacharya, B. Guillou, A. Li
{"title":"An $R$-motivic v1-self-map of periodicity $1$","authors":"P. Bhattacharya, B. Guillou, A. Li","doi":"10.4310/hha.2022.v24.n1.a15","DOIUrl":"https://doi.org/10.4310/hha.2022.v24.n1.a15","url":null,"abstract":"","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70434956","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
The homotopy types of $SU(n)$-gauge groups over $S^{2m}$ $S^{2m}$上$SU(n)$规范群的同伦类型
IF 0.5 4区 数学
Homology Homotopy and Applications Pub Date : 2022-01-01 DOI: 10.4310/hha.2022.v24.n1.a3
Sajjad Mohammadi
{"title":"The homotopy types of $SU(n)$-gauge groups over $S^{2m}$","authors":"Sajjad Mohammadi","doi":"10.4310/hha.2022.v24.n1.a3","DOIUrl":"https://doi.org/10.4310/hha.2022.v24.n1.a3","url":null,"abstract":"","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70435013","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: 1
Optimal colored Tverberg theorems for prime powers 素数幂的最优着色Tverberg定理
IF 0.5 4区 数学
Homology Homotopy and Applications Pub Date : 2022-01-01 DOI: 10.4310/hha.2022.v24.n2.a4
D. Jojic, G. Panina, R. Živaljević
{"title":"Optimal colored Tverberg theorems for prime powers","authors":"D. Jojic, G. Panina, R. Živaljević","doi":"10.4310/hha.2022.v24.n2.a4","DOIUrl":"https://doi.org/10.4310/hha.2022.v24.n2.a4","url":null,"abstract":"","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70435065","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: 1
Multicategories model all connective spectra 多类别为所有连接谱建模
IF 0.5 4区 数学
Homology Homotopy and Applications Pub Date : 2021-11-16 DOI: 10.4310/HHA.2023.v25.n1.a8
Niles Johnson, Donald Yau
{"title":"Multicategories model all connective spectra","authors":"Niles Johnson, Donald Yau","doi":"10.4310/HHA.2023.v25.n1.a8","DOIUrl":"https://doi.org/10.4310/HHA.2023.v25.n1.a8","url":null,"abstract":"There is a free construction from multicategories to permutative categories, left adjoint to the endomorphism multicategory construction. The main result shows that these functors induce an equivalence of homotopy theories. This result extends a similar result of Thomason, that permutative categories model all connective spectra.","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42232059","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
Magnitude homology of graphs and discrete Morse theory on Asao–Izumihara complexes Asao–Izumihara复形图的幅同源性和离散Morse理论
IF 0.5 4区 数学
Homology Homotopy and Applications Pub Date : 2021-10-06 DOI: 10.4310/hha.2023.v25.n1.a17
Yusuke Tajima, M. Yoshinaga
{"title":"Magnitude homology of graphs and discrete Morse theory on Asao–Izumihara complexes","authors":"Yusuke Tajima, M. Yoshinaga","doi":"10.4310/hha.2023.v25.n1.a17","DOIUrl":"https://doi.org/10.4310/hha.2023.v25.n1.a17","url":null,"abstract":"Recently, Asao and Izumihara introduced CW-complexes whose homology groups are isomorphic to direct summands of the graph magnitude homology group. In this paper, we study the homotopy type of the CW-complexes in connection with the diagonality of magnitude homology groups. We prove that the Asao-Izumihara complex is homotopy equivalent to a wedge of spheres for pawful graphs introduced by Y. Gu. The result can be considered as a homotopy type version of Gu's result. We also formulate a slight generalization of the notion of pawful graphs and find new non-pawful diagonal graphs of diameter $2$.","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48686829","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: 3
Path homology of directed hypergraphs 有向超图的路径同调
IF 0.5 4区 数学
Homology Homotopy and Applications Pub Date : 2021-09-20 DOI: 10.4310/hha.2022.v24.n2.a18
Y. Muranov, A. Szczepkowska, V. Vershinin
{"title":"Path homology of directed hypergraphs","authors":"Y. Muranov, A. Szczepkowska, V. Vershinin","doi":"10.4310/hha.2022.v24.n2.a18","DOIUrl":"https://doi.org/10.4310/hha.2022.v24.n2.a18","url":null,"abstract":"We describe various path homology theories constructed for a directed hypergraph. We introduce the category of directed hypergraphs and the notion of a homotopy in this category. Also, we investigate the functoriality and the homotopy invariance of the introduced path homology groups. We provide examples of computation of these homology groups.","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49395011","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
Derived universal Massey products 衍生通用Massey产品
IF 0.5 4区 数学
Homology Homotopy and Applications Pub Date : 2021-09-03 DOI: 10.4310/hha.2023.v25.n1.a10
F. Muro
{"title":"Derived universal Massey products","authors":"F. Muro","doi":"10.4310/hha.2023.v25.n1.a10","DOIUrl":"https://doi.org/10.4310/hha.2023.v25.n1.a10","url":null,"abstract":"We define an obstruction to the formality of a differential graded algebra over a graded operad defined over a commutative ground ring. This obstruction lives in the derived operadic cohomology of the algebra. Moreover, it determines all operadic Massey products induced on the homology algebra, hence the name of derived universal Massey product.","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41935531","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
Constructing coproducts in locally Cartesian closed $infty$-categories 构造局部笛卡尔闭$infty$ -范畴中的余积
IF 0.5 4区 数学
Homology Homotopy and Applications Pub Date : 2021-08-25 DOI: 10.4310/hha.2023.v25.n1.a4
Jonas Frey, Nima Rasekh
{"title":"Constructing coproducts in locally Cartesian closed $infty$-categories","authors":"Jonas Frey, Nima Rasekh","doi":"10.4310/hha.2023.v25.n1.a4","DOIUrl":"https://doi.org/10.4310/hha.2023.v25.n1.a4","url":null,"abstract":"We prove that every locally Cartesian closed $infty$-category with subobject classifier has a strict initial object and disjoint and universal binary coproducts.","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47014450","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
E-infinity structure in hyperoctahedral homology 超八面体同源中的E-无穷大结构
IF 0.5 4区 数学
Homology Homotopy and Applications Pub Date : 2021-08-11 DOI: 10.4310/HHA.2023.v25.n1.a1
Daniel F. Graves
{"title":"E-infinity structure in hyperoctahedral homology","authors":"Daniel F. Graves","doi":"10.4310/HHA.2023.v25.n1.a1","DOIUrl":"https://doi.org/10.4310/HHA.2023.v25.n1.a1","url":null,"abstract":"Hyperoctahedral homology for involutive algebras is the homology theory associated to the hyperoctahedral crossed simplicial group. It is related to equivariant stable homotopy theory via the homology of equivariant infinite loop spaces. In this paper we show that there is an E-infinity algebra structure on the simplicial module that computes hyperoctahedral homology. We deduce that hyperoctahedral homology admits Dyer-Lashof homology operations. Furthermore, there is a Pontryagin product which gives hyperoctahedral homology the structure of an associative, graded-commutative algebra. We also give an explicit description of hyperoctahedral homology in degree zero. Combining this description and the Pontryagin product we show that hyperoctahedral homology fails to preserve Morita equivalence.","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45512129","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
Ranks of homotopy and cohomology groups for rationally elliptic spaces and algebraic varieties 合理椭圆空间与代数变异的同伦与上同调群的行列
IF 0.5 4区 数学
Homology Homotopy and Applications Pub Date : 2021-07-24 DOI: 10.4310/HHA.2022.v24.n2.a5
A. Libgober, Shoji Yokura
{"title":"Ranks of homotopy and cohomology groups for rationally elliptic spaces and algebraic varieties","authors":"A. Libgober, Shoji Yokura","doi":"10.4310/HHA.2022.v24.n2.a5","DOIUrl":"https://doi.org/10.4310/HHA.2022.v24.n2.a5","url":null,"abstract":"We discuss inequalities between the values of emph{homotopical and cohomological Poincar'e polynomials} of the self-products of rationally elliptic spaces. For rationally elliptic quasi-projective varieties, we prove inequalities between the values of generating functions for the ranks of the graded pieces of the weight and Hodge filtrations of the canonical mixed Hodge structures on homotopy and cohomology groups. Several examples of such mixed Hodge polynomials and related inequalities for rationally elliptic quasi-projective algebraic varieties are presented. One of the consequences is that the homotopical (resp. cohomological) mixed Hodge polynomial of a rationally elliptic toric manifold is a sum (resp. a product) of polynomials of projective spaces. We introduce an invariant called emph{stabilization threshold} $frak{pp} (X;varepsilon)$ for a simply connected rationally elliptic space $X$ and a positive real number $varepsilon$, and we show that the Hilali conjecture implies that $frak{pp} (X;1) le 3$.","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48109773","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
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