A splicing formula for Casson-Walker's invariant
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.
scientific article; zbMATH DE number 537300
scientific article