A splicing formula for Casson-Walker's invariant
type: Item
instance of: scholarly article
title: A splicing formula for Casson-Walker's invariant
zbMATH Open document ID: 0793.57007
DOI: 10.1007/BF01445108
author: V. Pereyra
published in: Mathematische Annalen
publication date: 1994-08-25T00:00:00Z
full work available at URL: https://eudml.org/doc/165088
review text: Casson's \(\mathbb{Z}\)-valued invariant for a \(\mathbb{Z} HS\) (a homology sphere) was extended to a \(\mathbb{Q}\)-valued invariant for a \(\mathbb{Q} HS\) (a rational homology sphere) by \textit{K. Walker} [Thesis, University of California at Berkeley (1990)]. \textit{S. Akbulut} and \textit{J. D. McCarthy} [Casson's invariant for oriented homology 3-spheres, Mathematical Notes, 36. Princeton, NJ (1990; Zbl 0695.57011)], \textit{S. Boyer} and \textit{A. Nicas} [Trans. Am. Math. Soc. 322, No. 2, 507-522 (1990; Zbl 0707.57009)], \textit{S. Fukuhara} and \textit{N. Maruyama} [Tokyo J. Math. 11, No. 2, 281-287 (1988; Zbl 0675.57008)] have independently proved that Casson's invariant is additive under splicing. In this paper we derive a formula of splicing for Casson-Walker's invariant, and see that the Dedekind sum comes out as a difference.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 537300
zbMATH Keywords: Casson's invariant
zbMATH Keywords: splicing for Casson-Walker invariant
zbMATH Keywords: rational homology sphere
zbMATH Keywords: splicing
zbMATH Keywords: Dedekind sum
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 537300