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.
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
@article{AIF_2004__54_4_1107_0, author = {Perron, Bernard}, title = {Mapping class group and the {Casson} invariant}, journal = {Annales de l'Institut Fourier}, pages = {1107--1138}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {4}, year = {2004}, doi = {10.5802/aif.2045}, mrnumber = {2111023}, zbl = {02162421}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2045/} }
TY - JOUR AU - Perron, Bernard TI - Mapping class group and the Casson invariant JO - Annales de l'Institut Fourier PY - 2004 SP - 1107 EP - 1138 VL - 54 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2045/ DO - 10.5802/aif.2045 LA - en ID - AIF_2004__54_4_1107_0 ER -
%0 Journal Article %A Perron, Bernard %T Mapping class group and the Casson invariant %J Annales de l'Institut Fourier %D 2004 %P 1107-1138 %V 54 %N 4 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2045/ %R 10.5802/aif.2045 %G en %F AIF_2004__54_4_1107_0
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://archive.numdam.org/articles/10.5802/aif.2045/
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