{"title":"曲线模空间上的一个新的上同调类","authors":"Paul Norbury","doi":"10.2140/gt.2023.27.2695","DOIUrl":null,"url":null,"abstract":"We define a collection of cohomology classes $\\Theta_{g,n}\\in H^{4g-4+2n}(\\overline{\\cal M}_{g,n})$ for $2g-2+n>0$ that restrict naturally to boundary divisors. We prove that a generating function for the intersection numbers $\\int_{\\overline{\\cal M}_{g,n}}\\Theta_{g,n}\\prod_{i=1}^n\\psi_i^{m_i}$ is a tau function of the KdV hierarchy. This is analogous to the theorem conjectured by Witten and proven by Kontsevich that a generating function for the intersection numbers $\\int_{\\overline{\\cal M}_{g,n}}\\prod_{i=1}^n\\psi_i^{m_i}$ is a tau function of the KdV hierarchy.","PeriodicalId":49200,"journal":{"name":"Geometry & Topology","volume":"98 1","pages":"0"},"PeriodicalIF":1.7000,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"38","resultStr":"{\"title\":\"A new cohomology class on the moduli space of curves\",\"authors\":\"Paul Norbury\",\"doi\":\"10.2140/gt.2023.27.2695\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We define a collection of cohomology classes $\\\\Theta_{g,n}\\\\in H^{4g-4+2n}(\\\\overline{\\\\cal M}_{g,n})$ for $2g-2+n>0$ that restrict naturally to boundary divisors. We prove that a generating function for the intersection numbers $\\\\int_{\\\\overline{\\\\cal M}_{g,n}}\\\\Theta_{g,n}\\\\prod_{i=1}^n\\\\psi_i^{m_i}$ is a tau function of the KdV hierarchy. This is analogous to the theorem conjectured by Witten and proven by Kontsevich that a generating function for the intersection numbers $\\\\int_{\\\\overline{\\\\cal M}_{g,n}}\\\\prod_{i=1}^n\\\\psi_i^{m_i}$ is a tau function of the KdV hierarchy.\",\"PeriodicalId\":49200,\"journal\":{\"name\":\"Geometry & Topology\",\"volume\":\"98 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2023-09-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"38\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geometry & Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/gt.2023.27.2695\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geometry & Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/gt.2023.27.2695","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
A new cohomology class on the moduli space of curves
We define a collection of cohomology classes $\Theta_{g,n}\in H^{4g-4+2n}(\overline{\cal M}_{g,n})$ for $2g-2+n>0$ that restrict naturally to boundary divisors. We prove that a generating function for the intersection numbers $\int_{\overline{\cal M}_{g,n}}\Theta_{g,n}\prod_{i=1}^n\psi_i^{m_i}$ is a tau function of the KdV hierarchy. This is analogous to the theorem conjectured by Witten and proven by Kontsevich that a generating function for the intersection numbers $\int_{\overline{\cal M}_{g,n}}\prod_{i=1}^n\psi_i^{m_i}$ is a tau function of the KdV hierarchy.
期刊介绍:
Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers.
The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.