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

2009/11/01 by SANG YOUL LEE, Sang Youl Lee, MYOUNGSOO SEO +1
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Combinatorial Mathematics

paper · doi:10.1142/s0218216509007610

Abstract

In this paper, we introduce a representation of knots and links in S 3 by integral matrices and then give an explicit formula for the Casson invariant for integral homology 3-spheres obtained from S 3 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.

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