{"title":"Polyhedral products in abstract and motivic homotopy theory","authors":"William Hornslien","doi":"arxiv-2406.13540","DOIUrl":null,"url":null,"abstract":"We introduce polyhedral products in an $\\infty$-categorical setting. We\ngeneralize a splitting result by Bahri, Bendersky, Cohen, and Gitler that\ndetermines the stable homotopy type of the a polyhedral product. We also\nintroduce a motivic refinement of moment-angle complexes and use the splitting\nresult to compute cellular $\\mathbb{A}^1$-homology, and $\\mathbb{A}^1$-Euler\ncharacteristics.","PeriodicalId":501119,"journal":{"name":"arXiv - MATH - Algebraic Topology","volume":"45 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-19","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-2406.13540","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 introduce polyhedral products in an $\infty$-categorical setting. We
generalize a splitting result by Bahri, Bendersky, Cohen, and Gitler that
determines the stable homotopy type of the a polyhedral product. We also
introduce a motivic refinement of moment-angle complexes and use the splitting
result to compute cellular $\mathbb{A}^1$-homology, and $\mathbb{A}^1$-Euler
characteristics.
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