{"title":"与二维简单复数相关的矩角复数的环空间分解","authors":"Lewis Stanton","doi":"arxiv-2407.10781","DOIUrl":null,"url":null,"abstract":"We show that the loop space of a moment-angle complex associated to a\n$2$-dimensional simplicial complex decomposes as a finite type product of\nspheres, loops on spheres, and certain indecomposable spaces which appear in\nthe loop space decomposition of Moore spaces. We also give conditions on\ncertain subcomplexes under which, localised away from sufficiently many primes,\nthe loop space of a moment-angle complex decomposes as a finite type product of\nspheres and loops on spheres.","PeriodicalId":501119,"journal":{"name":"arXiv - MATH - Algebraic Topology","volume":"45 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Loop space decompositions of moment-angle complexes associated to two dimensional simplicial complexes\",\"authors\":\"Lewis Stanton\",\"doi\":\"arxiv-2407.10781\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the loop space of a moment-angle complex associated to a\\n$2$-dimensional simplicial complex decomposes as a finite type product of\\nspheres, loops on spheres, and certain indecomposable spaces which appear in\\nthe loop space decomposition of Moore spaces. We also give conditions on\\ncertain subcomplexes under which, localised away from sufficiently many primes,\\nthe loop space of a moment-angle complex decomposes as a finite type product of\\nspheres and loops on spheres.\",\"PeriodicalId\":501119,\"journal\":{\"name\":\"arXiv - MATH - Algebraic Topology\",\"volume\":\"45 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-15\",\"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-2407.10781\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.10781","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Loop space decompositions of moment-angle complexes associated to two dimensional simplicial complexes
We show that the loop space of a moment-angle complex associated to a
$2$-dimensional simplicial complex decomposes as a finite type product of
spheres, loops on spheres, and certain indecomposable spaces which appear in
the loop space decomposition of Moore spaces. We also give conditions on
certain subcomplexes under which, localised away from sufficiently many primes,
the loop space of a moment-angle complex decomposes as a finite type product of
spheres and loops on spheres.