Actions of groups of diffeomorphisms on one-manifolds
Shigenori Matsumoto

TL;DR
This paper proves that for certain closed manifolds fibering over spheres, any group homomorphism from their diffeomorphism groups to the homeomorphism group of the real line is trivial, revealing rigidity in their group actions.
Contribution
It establishes the triviality of homomorphisms from diffeomorphism groups of specific manifolds to the homeomorphism group of the line, extending understanding of group action rigidity.
Findings
Homomorphisms from $ ext{Diff}_c(M)_0$ to $ ext{Homeo}( eal)$ are trivial for manifolds fibering over spheres.
Demonstrates rigidity of diffeomorphism groups acting on the real line.
Provides new insights into the structure of diffeomorphism groups of fibered manifolds.
Abstract
Denote by the identity component of the group of compactly supported diffeomorphisms of a connected manifold , and by the group of the homeomorphisms of . We show that if is a closed manifold which fibers over (), then any homomorphism from to is trivial.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric and Algebraic Topology · Advanced Topology and Set Theory
