{"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":49605,"journal":{"name":"Revista Matematica Complutense","volume":null,"pages":null},"PeriodicalIF":1.4000,"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\":49605,\"journal\":{\"name\":\"Revista Matematica Complutense\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.4000,\"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\":\"Revista Matematica Complutense\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s13163-019-00297-z\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2019/5/5 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Matematica Complutense","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13163-019-00297-z","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2019/5/5 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","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:
Revista Matemática Complutense is an international research journal supported by the School of Mathematics at Complutense University in Madrid. It publishes high quality research and survey articles across pure and applied mathematics. Fields of interests include: analysis, differential equations and applications, geometry, topology, algebra, statistics, computer sciences and astronomy. This broad interest is reflected in our interdisciplinary editorial board which is comprised of over 30 internationally esteemed researchers in diverse areas.
The Editorial Board of Revista Matemática Complutense organizes the “Santaló Lecture”, a yearly event where a distinguished mathematician is invited to present a lecture at Complutense University and contribute to the journal. Past lecturers include: Charles T.C. Wall, Jack K. Hale, Hans Triebel, Marcelo Viana, Narayanswamy Balakrishnan, Nigel Kalton, Alfio Quarteroni, David E. Edmunds, Giuseppe Buttazzo, Juan L. Vázquez, Eduard Feireisl, Nigel Hitchin, Lajos Horváth, Hélène Esnault, Luigi Ambrosio, Ignacio Cirac and Bernd Sturmfels. The Santaló Lecturer for 2019 will be Noel Cressie from National Institute for Applied Statistics Research Australia (NIASRA), University of Wollongong.