Actions of groups of diffeomorphisms on one-manifolds

preprint2013arXivOpen access

Abstract

Denote by $\DC(M)_0$ the identity component of the group of compactly supported C∞C^\infty diffeomorphisms of a connected C∞C^\infty manifold MM, and by $\HR$ the group of the homeomorphisms of R\R. We show that if MM is a closed manifold which fibers over SmS^m (m≥2m\geq 2), then any homomorphism from $\DC(M)_0$ to $\HR$ is trivial.

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