Mapping class group and the Casson invariant
Annales de l'Institut Fourier, Volume 54 (2004) no. 4, pp. 1107-1138.

Using a new definition of the second and third Johsnon homomorphisms, we simplify and extend the work of Morita on the Casson invariant of homology-spheres defined by Heegard splittings. In particular, we calculate the Casson invariant of the homology-sphere obtained by gluing two handlebodies along a homeomorphism of the boundary belonging to the Torelli subgroup.

En utilisant une nouvelle définition des second et troisième homomorphismes de Johnson, on simplifie et on généralise les résultats de Morita sur l'invariant de Casson des sphères d'homologie définies par scindement de Heegard. En particulier, on calcule l'invariant de Casson des sphères d'homologie obtenues en recollant deux corps d'anses par un homéomorphisme du groupe de Torelli.

DOI: 10.5802/aif.2045
Classification: 57M05
Keywords: mapping class group, Johnson-Morita homomorphisms, homology spheres, Casson invariant
Perron, Bernard 1

1 Université de Bourgogne, Institut de mathématiques de Bourgogne, UFR sciences et techniques, 9 avenue Alain Savary, BP 47870, 21078 Dijon cedex (France)
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Perron, Bernard. Mapping class group and the Casson invariant. Annales de l'Institut Fourier, Volume 54 (2004) no. 4, pp. 1107-1138. doi : 10.5802/aif.2045. http://www.numdam.org/articles/10.5802/aif.2045/

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