A remark on the contactomorphism group of overtwisted contact spheres

Eduardo Fernández; Fabio Gironella

doi:10.5802/crmath.32

Géométrie, Topologie

A remark on the contactomorphism group of overtwisted contact spheres
[Une remarque sur le groupe des contactomorphismes des sphères de contact vrillées]

Eduardo Fernández ¹ ; Fabio Gironella ²

¹ Universidad Complutense de Madrid, Departamento de Álgebra, Geometría y Topología, Facultad de Matemáticas, and Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Madrid, Spain
² Alfréd Rényi Institute of Mathematics, Budapest, Hungary

Comptes Rendus. Mathématique, Volume 358 (2020) no. 2, pp. 189-196.

Résumé
Abstract

On prouve l’existence d’éléments d’ordre infini dans certains groupes d’homotopie du groupe des contactomorphismes des sphères vrillées. En particulier, il s’en suit que le groupe des contactomorphismes de certaines sphères vrillées n’est pas homotopiquement équivalent à un groupe de Lie de dimension finie.

We show the existence of elements of infinite order in some homotopy groups of the contactomorphism group of overtwisted spheres. It follows in particular that the contactomorphism group of some high dimensional overtwisted spheres is not homotopically equivalent to a finite dimensional Lie group.

Reçu le : 2019-10-27
Révisé le : 2020-02-28
Accepté le : 2020-03-03
Publié le : 2020-06-15

DOI : 10.5802/crmath.32

Affiliations des auteurs :

Eduardo Fernández ¹ ; Fabio Gironella ²

¹ Universidad Complutense de Madrid, Departamento de Álgebra, Geometría y Topología, Facultad de Matemáticas, and Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Madrid, Spain
² Alfréd Rényi Institute of Mathematics, Budapest, Hungary

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {A remark on the contactomorphism group of overtwisted contact spheres},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {189--196},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {2},
     year = {2020},
     doi = {10.5802/crmath.32},
     language = {en},
}

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Eduardo Fernández; Fabio Gironella. A remark on the contactomorphism group of overtwisted contact spheres. Comptes Rendus. Mathématique, Volume 358 (2020) no. 2, pp. 189-196. doi : 10.5802/crmath.32. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.32/

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