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VOL. 52 | 2008 On the simplicity of the group of contactomorphisms
Takashi Tsuboi

Editor(s) Robert Penner, Dieter Kotschick, Takashi Tsuboi, Nariya Kawazumi, Teruaki Kitano, Yoshihiko Mitsumatsu

## Abstract

We consider the group $\mathrm{Cont}_c^r (M^{2n+1}, \alpha)$ of $C^r$ contactomorphisms with compact support of a contact manifold $(M^{2n+1}, \alpha)$ of dimension $(2n+1)$ with the $C^r$ topology. We show that the first homology group of the classifying space $B \overline{\mathrm{Cont}}{}_c^r (M^{2n+1}, \alpha)$ for the $C^r$ foliated $M^{2n+1}$ products with compact support with transverse contact structure $\alpha$ is trivial for $1 \le r \lt n+(3/2)$. This implies that the identity component $\mathrm{Cont}_c^r (M^{2n+1}, \alpha)_0$ of the group $\mathrm{Cont}_c^r (M^{2n+1}, \alpha)$ of contactomorphisms with compact support of a connected contact manifold $(M^{2n+1}, \alpha)$ is a simple group for $1 \le r \lt n+(3/2)$.

## Information

Published: 1 January 2008
First available in Project Euclid: 28 November 2018

zbMATH: 1161.57014
MathSciNet: MR2509723

Digital Object Identifier: 10.2969/aspm/05210491

Subjects:
Primary: 57R32, 57R50
Secondary: 57R17, 57R52

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