Product formulas along \(T^3\) for Seiberg-Witten invariants
type: Item
instance of: scholarly article
title: Product formulas along \(T^3\) for Seiberg-Witten invariants
zbMATH Open document ID: 0892.57021
author: John W. Morgan
author: T. S. Mrowka
author: Zoltán Szabó
published in: Mathematical Research Letters
publication date: 1998-03-18T00:00:00Z
review text: Let \(X\) be a smooth closed 4-manifold which contains a smoothly embedded 2-torus \(T^2\) with trivial self-intersection number. If \(N\) is a regular neighborhood of \(T^2\) in \(X\) and \(Y\) is the closure of the complement of \(N\) in \(X\), let \(a,b,c\) denote the elements of a basis in \(H_1(\partial Y;\mathbb{Z})\). For each indivisible class \(\gamma= pa+qb +rc\), consider an orientation reversing diffeomorphism \(f_\gamma =\partial (D^2\times T^2) \to\partial Y\) with \((f_\gamma)_* [\partial (D^2 \times pt)] =\gamma\). The authors find interesting relations between the Seiberg-Witten invariants of the manifolds obtained by Dehn-Montesinos surgery along \(T^2\), i.e. manifolds of type \(X_\gamma =Y\cup_{f_\gamma} (D^2 \times T^2)\).
Mathematics Subject Classification ID: 57R57
Mathematics Subject Classification ID: 57N13
zbMATH DE Number: 1130628
zbMATH Keywords: smooth 4-manifolds
zbMATH Keywords: embedded 2-torus
zbMATH Keywords: Seiberg-Witten invariants
zbMATH Keywords: Dehn-Montesinos surgery
reviewed by: Alberto Cavicchioli
MaRDI profile type: Publication
Wikidata QID: Q102358785
full work available at URL: mrl.1997.v4.n6.a11
OpenAlex ID: W2029255895
DOI: 10.4310/MRL.1997.V4.N6.A11
description: scientific article; zbMATH DE number 1130628