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Coeur de l'invariant de Casson et cobordismes d'homologie

Abstract : The Casson invariant is a classical invariant of integral homology 3-spheres. S. Morita described it as a sum of two homomorphisms d and q defined on a subgroup K_(g,1) of the mapping class group M_(g,1) of a oriented surface S_(g,1) of genus g with one boundary component. The homomorphism d can be viewed as the core of the Casson invariant and is described geometrically in terms of SU-framings on mapping torii. At the beginning, d comes from an application d_X defined on M_(g,1) as the difference between the
Meyer cocycle and an intersection cocycle which depends on a non singular vector field X on the surface S_(g,1). First, we will consider the homology cobordisms and their associated group H_(g,1) : via the mapping cylinders, M_(g,1) is a subgroup of H_(g,1). In prospect of extending d, we will extend the intersection cocycles and Meyer cocycle to homology cobordisms equipped with relative Euler structure.
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Contributor : Kristell Dequidt Picot <>
Submitted on : Wednesday, July 20, 2005 - 1:39:38 PM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
Long-term archiving on: : Friday, April 2, 2010 - 10:44:54 PM


  • HAL Id : tel-00009786, version 1



Kristell Dequidt Picot. Coeur de l'invariant de Casson et cobordismes d'homologie. Mathématiques [math]. Université de Nantes, 2005. Français. ⟨tel-00009786⟩



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