管道3流形Seiberg-Witten不变量的手术公式。

IF 1.4 3区数学 Q1 MATHEMATICS Revista Matematica Complutense Pub Date : 2020-01-01 Epub Date: 2019-05-05 DOI:10.1007/s13163-019-00297-z

Tamás László, János Nagy, András Némethi

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引用次数: 12

摘要

设M (T)是与连通负定图T相关联的有理同调球垂3流形。考虑与T相关的组合多变量庞卡罗级数及其计数函数，它们包含丰富的拓扑信息。使用级数的“周期常数”(具有与顶点集合的任意子集I相关的约简变量)，我们证明了归一化Seiberg-Witten不变量的运算公式:与I相关的周期常数表现为M (T)和M (T \ I)对任意I的Seiberg-Witten不变量的差。

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Surgery formulae for the Seiberg-Witten invariant of plumbed 3-manifolds.

Assume that $M (T)$ is a rational homology sphere plumbed 3-manifold associated with a connected negative definite graph $T$ . We consider the combinatorial multivariable Poincaré series associated with $T$ and its counting functions, which encode rich topological information. Using the 'periodic constant' of the series (with reduced variables associated with an arbitrary subset $I$ of the set of vertices) we prove surgery formulae for the normalized Seiberg-Witten invariants: the periodic constant associated with $I$ appears as the difference of the Seiberg-Witten invariants of $M (T)$ and $M (T \ I)$ for any $I$ .

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来源期刊

Revista Matematica Complutense 数学-数学

CiteScore

2.30

自引率

0.00%

发文量

审稿时长

>12 weeks

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.

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