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FORMULAS FOR THE CASSON INVARIANT OF CERTAIN INTEGRAL HOMOLOGY 3-SPHERES

SANG YOUL LEE

Department of Mathematics, Pusan National University, Pusan 609-735, Korea

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and

MYOUNGSOO SEO

Department of Mathematics, Kyungpook National University, Daegu 702-701, Korea

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https://doi.org/10.1142/S0218216509007610Cited by:2 (Source: Crossref)

Abstract

In this paper, we introduce a representation of knots and links in S³ by integral matrices and then give an explicit formula for the Casson invariant for integral homology 3-spheres obtained from S³ by Dehn surgery along the knots and links represented by the integral matrices in which either all entries are even or the entries of each row are the same odd number. As applications, we study the preimage of the Casson invariant for a given integer and also give formulas for the Casson invariants of some special classes of integral homology 3-spheres.

Keywords:

AMSC: 57M25, 57M27

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