Seiberg-Witten and Casson-Walker invariants for rational homology 3-spheres
type: Item
instance of: scholarly article
title: Seiberg-Witten and Casson-Walker invariants for rational homology 3-spheres
zbMATH Open document ID: 0994.57027
DOI: 10.1023/A:1016299716922
author: Matilde Marcolli
author: Bai-Ling Wang
published in: Geometriae Dedicata
publication date: 2002-08-21T00:00:00Z
review text: This paper considers a modified version of the Seiberg-Witten invariants for rational homology 3-spheres, obtained by adding to the original invariants a correction term which is a combination of \(\eta\)-invariants. Then it is shown that these modified invariants are topological invariants. This is achieved by showing how they behave under surgery on a knot in a rational homology 3-sphere, by using the results in [\textit{A. Carey, M. Marcolli} and \textit{B. L. Wang}, The geometric triangle for 3-dimensional Seiberg-Witten monopoles, Preprint math.DG/9907065]. The sum of these modified Seiberg-Witten invariants over all \(\text{spin}^c\) structures of the rational homology 3-sphere \(Y\) is \(|H_{1}(Y;Z)|/2\) times the Casson-Walker invariant of \(Y\).
reviewed by: Vicente Muñoz
Mathematics Subject Classification ID: 57R57
Mathematics Subject Classification ID: 57M27
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 1786837
zbMATH Keywords: Seiberg-Witten
zbMATH Keywords: Casson-Walker
zbMATH Keywords: knot surgery
MaRDI profile type: Publication
full work available at URL: a:1016299716922
OpenAlex ID: W2131776873
Wikidata QID: Q60020329
description: scientific article; zbMATH DE number 1786837