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Denote by $DC(M)_0$ the identity component of the group of compactly supported $C^infty$ diffeomorphisms of a connected $C^infty$ manifold $M$, and by $HR$ the group of the homeomorphisms of $R$. We show that if $M$ is a closed manifold which fibers over $S^m$ ($mgeq 2$), then any homomorphism from $DC(M)_0$ to $HR$ is trivial.
Denote by $DC(M)_0$ the identity component of the group of the compactly supported $C^r$ diffeomorphisms of a connected $C^infty$ manifold $M$. We show that if $dim(M)geq2$ and $r eq dim(M)+1$, then any homomorphism from $DC(M)_0$ to ${Diff}^1(R)$ or ${Diff}^1(S^1)$ is trivial.
In this article, we construct countably many mutually non-isotopic diffeomorphisms of some closed non simply-connected 4-manifolds that are homotopic to but not isotopic to the identity, by surgery along $Theta$-graphs. As corollaries of this, we obt
According to the work of Laitinen, Morimoto, Oliver and Pawal{}owski, a finite group $G$ has a smooth effective one fixed point action on some sphere if and only if $G$ is an Oliver group. For some finite Oliver groups $G$ of order up to $216$, and f
If $G$ is a free product of finite groups, let $Sigma Aut_1(G)$ denote all (necessarily symmetric) automorphisms of $G$ that do not permute factors in the free product. We show that a McCullough-Miller [D. McCullough and A. Miller, {em Symmetric Auto
This note deals with arbitrary Morse-Smale diffeomorphisms in dimension 3 and extends ideas from cite{GrLaPo}, cite{GrLaPo1}, where gradient-like case was considered. We introduce a kind of Morse-Lyapunov function, called dynamically ordered, which f