{"title":"曲率算子和有理共线性","authors":"Renato G. Bettiol , McFeely Jackson Goodman","doi":"10.1016/j.aim.2024.109995","DOIUrl":null,"url":null,"abstract":"<div><div>We determine linear inequalities on the eigenvalues of curvature operators that imply vanishing of the twisted <span><math><mover><mrow><mi>A</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> genus on a closed Riemannian spin manifold, where the twisting bundle is any prescribed parallel bundle of tensors. These inequalities yield surgery-stable curvature conditions tailored to annihilate further rational cobordism invariants, such as the Witten genus, elliptic genus, signature, and even the rational cobordism class itself.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109995"},"PeriodicalIF":1.5000,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Curvature operators and rational cobordism\",\"authors\":\"Renato G. Bettiol , McFeely Jackson Goodman\",\"doi\":\"10.1016/j.aim.2024.109995\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We determine linear inequalities on the eigenvalues of curvature operators that imply vanishing of the twisted <span><math><mover><mrow><mi>A</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> genus on a closed Riemannian spin manifold, where the twisting bundle is any prescribed parallel bundle of tensors. These inequalities yield surgery-stable curvature conditions tailored to annihilate further rational cobordism invariants, such as the Witten genus, elliptic genus, signature, and even the rational cobordism class itself.</div></div>\",\"PeriodicalId\":50860,\"journal\":{\"name\":\"Advances in Mathematics\",\"volume\":\"458 \",\"pages\":\"Article 109995\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-10-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0001870824005115\",\"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":"Advances in Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0001870824005115","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We determine linear inequalities on the eigenvalues of curvature operators that imply vanishing of the twisted genus on a closed Riemannian spin manifold, where the twisting bundle is any prescribed parallel bundle of tensors. These inequalities yield surgery-stable curvature conditions tailored to annihilate further rational cobordism invariants, such as the Witten genus, elliptic genus, signature, and even the rational cobordism class itself.
期刊介绍：
Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.
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