{"title":"管道3流形Seiberg-Witten不变量的手术公式。","authors":"Tamás László, János Nagy, András Némethi","doi":"10.1007/s13163-019-00297-z","DOIUrl":null,"url":null,"abstract":"<p><p>Assume that <math><mrow><mi>M</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo></mrow> </math> is a rational homology sphere plumbed 3-manifold associated with a connected negative definite graph <math><mi>T</mi></math> . We consider the combinatorial multivariable Poincaré series associated with <math><mi>T</mi></math> and its counting functions, which encode rich topological information. Using the 'periodic constant' of the series (with reduced variables associated with an arbitrary subset <math><mi>I</mi></math> of the set of vertices) we prove surgery formulae for the normalized Seiberg-Witten invariants: the periodic constant associated with <math><mi>I</mi></math> appears as the difference of the Seiberg-Witten invariants of <math><mrow><mi>M</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo></mrow> </math> and <math><mrow><mi>M</mi> <mo>(</mo> <mi>T</mi> <mo>\\</mo> <mi>I</mi> <mo>)</mo></mrow> </math> for any <math><mi>I</mi></math> .</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s13163-019-00297-z","citationCount":"12","resultStr":"{\"title\":\"Surgery formulae for the Seiberg-Witten invariant of plumbed 3-manifolds.\",\"authors\":\"Tamás László, János Nagy, András Némethi\",\"doi\":\"10.1007/s13163-019-00297-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>Assume that <math><mrow><mi>M</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo></mrow> </math> is a rational homology sphere plumbed 3-manifold associated with a connected negative definite graph <math><mi>T</mi></math> . We consider the combinatorial multivariable Poincaré series associated with <math><mi>T</mi></math> and its counting functions, which encode rich topological information. Using the 'periodic constant' of the series (with reduced variables associated with an arbitrary subset <math><mi>I</mi></math> of the set of vertices) we prove surgery formulae for the normalized Seiberg-Witten invariants: the periodic constant associated with <math><mi>I</mi></math> appears as the difference of the Seiberg-Witten invariants of <math><mrow><mi>M</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo></mrow> </math> and <math><mrow><mi>M</mi> <mo>(</mo> <mi>T</mi> <mo>\\\\</mo> <mi>I</mi> <mo>)</mo></mrow> </math> for any <math><mi>I</mi></math> .</p>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s13163-019-00297-z\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s13163-019-00297-z\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2019/5/5 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13163-019-00297-z","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2019/5/5 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Surgery formulae for the Seiberg-Witten invariant of plumbed 3-manifolds.
Assume that is a rational homology sphere plumbed 3-manifold associated with a connected negative definite graph . We consider the combinatorial multivariable Poincaré series associated with and its counting functions, which encode rich topological information. Using the 'periodic constant' of the series (with reduced variables associated with an arbitrary subset of the set of vertices) we prove surgery formulae for the normalized Seiberg-Witten invariants: the periodic constant associated with appears as the difference of the Seiberg-Witten invariants of and for any .
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
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