Given any compact manifold , we construct a non-empty open subset of the space of -diffeomorphisms and a dense subset such that the centralizer of every diffeomorphism in is uncountable, hence non-trivial.
Pour toute variété compacte, de dimension quelconque, nous construisons une partie non vide, ouverte dans l’espace des -difféomorphismes de , et un sous-ensemble dense en , constitué de difféomorphismes dont le centralisateur est non dénombrable, donc non trivial.
Keywords: trivial centralizer, trivial symmetries, Mather invariant
Mot clés : centralisateur trivial, symétries triviales, invariant de Mather
@article{ASENS_2008_4_41_6_925_0, author = {Bonatti, Christian and Crovisier, Sylvain and Vago, Gioia M. and Wilkinson, Amie}, title = {Local density of diffeomorphisms with large centralizers}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {925--954}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {Ser. 4, 41}, number = {6}, year = {2008}, doi = {10.24033/asens.2085}, mrnumber = {2504109}, zbl = {1163.58003}, language = {en}, url = {http://archive.numdam.org/articles/10.24033/asens.2085/} }
TY - JOUR AU - Bonatti, Christian AU - Crovisier, Sylvain AU - Vago, Gioia M. AU - Wilkinson, Amie TI - Local density of diffeomorphisms with large centralizers JO - Annales scientifiques de l'École Normale Supérieure PY - 2008 SP - 925 EP - 954 VL - 41 IS - 6 PB - Société mathématique de France UR - http://archive.numdam.org/articles/10.24033/asens.2085/ DO - 10.24033/asens.2085 LA - en ID - ASENS_2008_4_41_6_925_0 ER -
%0 Journal Article %A Bonatti, Christian %A Crovisier, Sylvain %A Vago, Gioia M. %A Wilkinson, Amie %T Local density of diffeomorphisms with large centralizers %J Annales scientifiques de l'École Normale Supérieure %D 2008 %P 925-954 %V 41 %N 6 %I Société mathématique de France %U http://archive.numdam.org/articles/10.24033/asens.2085/ %R 10.24033/asens.2085 %G en %F ASENS_2008_4_41_6_925_0
Bonatti, Christian; Crovisier, Sylvain; Vago, Gioia M.; Wilkinson, Amie. Local density of diffeomorphisms with large centralizers. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 41 (2008) no. 6, pp. 925-954. doi : 10.24033/asens.2085. http://archive.numdam.org/articles/10.24033/asens.2085/
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