{"title":"Distributional Lusternik-Schnirelmann category of manifolds","authors":"Ekansh Jauhari","doi":"arxiv-2408.11036","DOIUrl":null,"url":null,"abstract":"We obtain several sufficient conditions for the distributional LS-category\n(dcat) of closed manifolds to be maximum, i.e., equal to their classical\nLS-category (cat). This gives us many new computations of dcat, especially for\nessential manifolds and (generalized) connected sums. In the process, we also\ndetermine the dcat of closed 3-manifolds having torsion-free fundamental groups\nand some closed geometrically decomposable 4-manifolds. Finally, we extend some\nof our results to closed Alexandrov spaces and discuss their cat and dcat in\ndimension 3.","PeriodicalId":501119,"journal":{"name":"arXiv - MATH - Algebraic Topology","volume":"65 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.11036","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We obtain several sufficient conditions for the distributional LS-category
(dcat) of closed manifolds to be maximum, i.e., equal to their classical
LS-category (cat). This gives us many new computations of dcat, especially for
essential manifolds and (generalized) connected sums. In the process, we also
determine the dcat of closed 3-manifolds having torsion-free fundamental groups
and some closed geometrically decomposable 4-manifolds. Finally, we extend some
of our results to closed Alexandrov spaces and discuss their cat and dcat in
dimension 3.