Pub Date : 2021-01-01DOI: 10.4310/hha.2021.v23.n1.a13
T. Brazelton, Robert Burklund, Stephen McKean, M. Montoro, Morgan Opie
{"title":"The trace of the local $mathbb{A}^1$-degree","authors":"T. Brazelton, Robert Burklund, Stephen McKean, M. Montoro, Morgan Opie","doi":"10.4310/hha.2021.v23.n1.a13","DOIUrl":"https://doi.org/10.4310/hha.2021.v23.n1.a13","url":null,"abstract":"","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70434590","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}
Pub Date : 2021-01-01DOI: 10.4310/HHA.2021.V23.N2.A7
R'emi Bottinelli, T. Kaiser
{"title":"Magnitude homology, diagonality, and median spaces","authors":"R'emi Bottinelli, T. Kaiser","doi":"10.4310/HHA.2021.V23.N2.A7","DOIUrl":"https://doi.org/10.4310/HHA.2021.V23.N2.A7","url":null,"abstract":"","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70435321","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}
Pub Date : 2021-01-01DOI: 10.4310/hha.2021.v23.n1.a19
Zhongjian Zhu, Jianzhong Pan
{"title":"The local hyperbolicity of $mathbf{A}_n^2$-complexes","authors":"Zhongjian Zhu, Jianzhong Pan","doi":"10.4310/hha.2021.v23.n1.a19","DOIUrl":"https://doi.org/10.4310/hha.2021.v23.n1.a19","url":null,"abstract":"","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70434598","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}
Pub Date : 2021-01-01DOI: 10.4310/hha.2021.v23.n1.a9
Panagiotis Konstantis
{"title":"Vector bundles and cohomotopies of $operatorname{spin} 5$-manifolds","authors":"Panagiotis Konstantis","doi":"10.4310/hha.2021.v23.n1.a9","DOIUrl":"https://doi.org/10.4310/hha.2021.v23.n1.a9","url":null,"abstract":"","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70434676","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}
Pub Date : 2021-01-01DOI: 10.4310/HHA.2021.V23.N2.A9
Shi Rong, Pu Zhang
{"title":"Strong version of Snake Lemma in exact categories","authors":"Shi Rong, Pu Zhang","doi":"10.4310/HHA.2021.V23.N2.A9","DOIUrl":"https://doi.org/10.4310/HHA.2021.V23.N2.A9","url":null,"abstract":"","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70435335","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}
Pub Date : 2021-01-01DOI: 10.4310/hha.2021.v23.n1.a7
H. Thai
{"title":"The wedge family of the cohomology of the $mathbb{C}$-motivic Steenrod algebra","authors":"H. Thai","doi":"10.4310/hha.2021.v23.n1.a7","DOIUrl":"https://doi.org/10.4310/hha.2021.v23.n1.a7","url":null,"abstract":"","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70434665","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}
Pub Date : 2021-01-01DOI: 10.4310/hha.2021.v23.n2.a16
M. Batanin, David White
{"title":"Left Bousfield localization and Eilenberg–Moore categories","authors":"M. Batanin, David White","doi":"10.4310/hha.2021.v23.n2.a16","DOIUrl":"https://doi.org/10.4310/hha.2021.v23.n2.a16","url":null,"abstract":"","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70434716","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}
Pub Date : 2020-12-31DOI: 10.4310/hha.2023.v25.n1.a2
E. Aldrovandi, N. Ramachandran
Let $pi: X to S$ be a family of smooth projective curves, and let $L$ and $M$ be a pair of line bundles on $X$. We show that Deligne's line bundle $langle{L,M}rangle$ can be obtained from the $mathcal{K}_2$-gerbe $G_{L,M}$ constructed in a previous work by the authors via an integration along the fiber map for gerbes that categorifies the well known one arising from the Leray spectral sequence of $pi$. Our construction provides a full account of the biadditivity properties of $langle {L,M}rangle$. The functorial description of the low degree maps in the Leray spectral sequence for $pi$ we develop are of independent interest, and along the course we provide an example of their application to the Brauer group.
设$pi: X 到S$是光滑的投影曲线族，设$L$和$M$是$X$上的一对线束。我们证明了Deligne线束$langle{L,M}rangle$可以由作者在以前的工作中构造的$mathcal{K}_2$-gerbe $G_{L,M}$得到，这是通过对由$pi$的Leray谱序列产生的著名的gerbes纤维映射进行积分得到的。我们的构造充分说明了$ rangle {L,M}rangle$的双可加性。我们开发的$pi$的Leray谱序列中的低次映射的泛函描述具有独立的兴趣，并在课程中提供了它们在Brauer群中的应用示例。
{"title":"Fiber integration of gerbes and Deligne line bundles","authors":"E. Aldrovandi, N. Ramachandran","doi":"10.4310/hha.2023.v25.n1.a2","DOIUrl":"https://doi.org/10.4310/hha.2023.v25.n1.a2","url":null,"abstract":"Let $pi: X to S$ be a family of smooth projective curves, and let $L$ and $M$ be a pair of line bundles on $X$. We show that Deligne's line bundle $langle{L,M}rangle$ can be obtained from the $mathcal{K}_2$-gerbe $G_{L,M}$ constructed in a previous work by the authors via an integration along the fiber map for gerbes that categorifies the well known one arising from the Leray spectral sequence of $pi$. Our construction provides a full account of the biadditivity properties of $langle {L,M}rangle$. The functorial description of the low degree maps in the Leray spectral sequence for $pi$ we develop are of independent interest, and along the course we provide an example of their application to the Brauer group.","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45876607","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}
Pub Date : 2020-12-03DOI: 10.4310/hha.2022.v24.n2.a11
Jean-Yves Welschinger
We recently introduced a notion of tilings of the geometric realization of a finite simplicial complex and related those tilings to the discrete Morse theory of R. Forman, especially when they have the property to be shellable, a property shared by the classical shellable complexes. We now observe that every such tiling supports a quiver which is acyclic precisely when the tiling is shellable and then that every shelling induces two spectral sequences which converge to the (co)homology of the complex. Their first pages are free modules over the critical tiles of the tiling.
{"title":"Spectral sequences of a Morse shelling","authors":"Jean-Yves Welschinger","doi":"10.4310/hha.2022.v24.n2.a11","DOIUrl":"https://doi.org/10.4310/hha.2022.v24.n2.a11","url":null,"abstract":"We recently introduced a notion of tilings of the geometric realization of a finite simplicial complex and related those tilings to the discrete Morse theory of R. Forman, especially when they have the property to be shellable, a property shared by the classical shellable complexes. We now observe that every such tiling supports a quiver which is acyclic precisely when the tiling is shellable and then that every shelling induces two spectral sequences which converge to the (co)homology of the complex. Their first pages are free modules over the critical tiles of the tiling.","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46351056","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}
Pub Date : 2020-12-02DOI: 10.4310/HHA.2021.V23.N2.A10
Janina C. Letz
In the derived category of modules over a commutative noetherian ring a complex $G$ is said to generate a complex $X$ if the latter can be obtained from the former by taking summands and finitely many cones. The number of cones required in this process is the generation time of $X$. In this paper we present some local to global type results for computing this invariant, and discuss applications.
{"title":"Local to global principles for generation time over commutative noetherian rings","authors":"Janina C. Letz","doi":"10.4310/HHA.2021.V23.N2.A10","DOIUrl":"https://doi.org/10.4310/HHA.2021.V23.N2.A10","url":null,"abstract":"In the derived category of modules over a commutative noetherian ring a complex $G$ is said to generate a complex $X$ if the latter can be obtained from the former by taking summands and finitely many cones. The number of cones required in this process is the generation time of $X$. In this paper we present some local to global type results for computing this invariant, and discuss applications.","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42109048","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：