流形的科斯祖尔自对偶性

Pub Date : 2024-04-29 DOI:10.1112/topo.12334

Connor Malin

{"title":"流形的科斯祖尔自对偶性","authors":"Connor Malin","doi":"10.1112/topo.12334","DOIUrl":null,"url":null,"abstract":"We show that Koszul duality for operads in <math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>Top</mi>\n <mo>,</mo>\n <mo>×</mo>\n <mo>)</mo>\n </mrow>\n <annotation>$(\\mathrm{Top},\\times)$</annotation>\n </semantics></math> can be expressed via generalized Thom complexes. As an application, we prove the Koszul self-duality of the right module <math>\n <semantics>\n <msub>\n <mi>E</mi>\n <mi>M</mi>\n </msub>\n <annotation>$E_M$</annotation>\n </semantics></math> associated to a framed manifold <math>\n <semantics>\n <mi>M</mi>\n <annotation>$M$</annotation>\n </semantics></math>. We discuss implications for factorization homology, embedding calculus, and confirm an old conjecture of Ching on the relation of Goodwillie calculus to manifold calculus.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Koszul self-duality of manifolds\",\"authors\":\"Connor Malin\",\"doi\":\"10.1112/topo.12334\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that Koszul duality for operads in <math>\\n <semantics>\\n <mrow>\\n <mo>(</mo>\\n <mi>Top</mi>\\n <mo>,</mo>\\n <mo>×</mo>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$(\\\\mathrm{Top},\\\\times)$</annotation>\\n </semantics></math> can be expressed via generalized Thom complexes. As an application, we prove the Koszul self-duality of the right module <math>\\n <semantics>\\n <msub>\\n <mi>E</mi>\\n <mi>M</mi>\\n </msub>\\n <annotation>$E_M$</annotation>\\n </semantics></math> associated to a framed manifold <math>\\n <semantics>\\n <mi>M</mi>\\n <annotation>$M$</annotation>\\n </semantics></math>. We discuss implications for factorization homology, embedding calculus, and confirm an old conjecture of Ching on the relation of Goodwillie calculus to manifold calculus.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-04-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/topo.12334\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12334","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们证明了 ( Top , × ) $(\mathrm{Top},\times)$ 中操作数的科斯祖尔对偶性可以通过广义托姆复数来表达。作为应用，我们证明了与框架流形 M $M$ 相关联的右模块 E M $E_M$ 的科斯祖尔自对偶性。我们讨论了因式分解同调、嵌入微积分的意义，并证实了程氏关于古德威利微积分与流形微积分关系的一个古老猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

Koszul self-duality of manifolds

We show that Koszul duality for operads in $(Top, \times)$ can be expressed via generalized Thom complexes. As an application, we prove the Koszul self-duality of the right module $E_{M}$ associated to a framed manifold $M$ . We discuss implications for factorization homology, embedding calculus, and confirm an old conjecture of Ching on the relation of Goodwillie calculus to manifold calculus.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助