no. 4
Mapping class group and the Casson invariant
[Groupe d'homéotopie de surfaces et invariant de Casson]
Perron, Bernard1
1 Université de Bourgogne, Institut de mathématiques de Bourgogne, UFR sciences et techniques, 9 avenue Alain Savary, BP 47870, 21078 Dijon cedex (France)
Annales de l'Institut Fourier, Tome 54 (2004) no. 4, pp. 1107-1138.

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.

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.

DOI : 10.5802/aif.2045
Classification : 57M05
Keywords: mapping class group, Johnson-Morita homomorphisms, homology spheres, Casson invariant
Mot clés : groupe d'homéotopie, homomorphismes de Johnson-Morita, sphères d'homologie, invariant de Casson

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, Tome 54 (2004) no. 4, pp. 1107-1138. doi : 10.5802/aif.2045. https://aif.centre-mersenne.org/articles/10.5802/aif.2045/

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