{"title":"Koszul self-duality of manifolds","authors":"Connor Malin","doi":"10.1112/topo.12334","DOIUrl":null,"url":null,"abstract":"<p>We show that Koszul duality for operads in <span></span><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 <span></span><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 <span></span><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.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 2","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12334","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We show that Koszul duality for operads in can be expressed via generalized Thom complexes. As an application, we prove the Koszul self-duality of the right module associated to a framed manifold . We discuss implications for factorization homology, embedding calculus, and confirm an old conjecture of Ching on the relation of Goodwillie calculus to manifold calculus.
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。
期刊介绍：
The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal.
The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.
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