{"title":"抽象和动机同调理论中的多面体积","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":"{\"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}","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}
Polyhedral products in abstract and motivic homotopy theory
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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