Let M be a manifold and N a 1-dimensional manifold. Assuming that r=dim(M)+1, we show that any nontrivial homomorphism ρ:Diffcr(M)→Homeo(N) has a standard form: necessarily M is 1-dimensional, and there are countably many embeddings φi:M→N with disjoint images such that the action of ρ is conjugate (via the product of the φi) to the diagonal action of Diffcr(M) on M×M×⋯ on ⋃iφi(M), and trivial elsewhere. This solves a conjecture of Matsumoto. We also show that the groups Diffcr(M) have no countable index subgroups.
Classification :
57-XX, 37-XX, 54-XX
Mots-clés :
homeomorphism groups, diffeomorphism groups, group actions on a circle
Affiliations des auteurs :
Lei Chen
1
;
Kathryn Mann
2
1
University of Maryland, College Park, USA
2
Cornell University, Ithaca, USA
Lei Chen; Kathryn Mann. There are no exotic actions of diffeomorphism groups on 1-manifolds. Groups, geometry, and dynamics, Tome 17 (2023) no. 1, pp. 91-99. doi: 10.4171/ggd/658
@article{10_4171_ggd_658,
author = {Lei Chen and Kathryn Mann},
title = {There are no exotic actions of diffeomorphism groups on 1-manifolds},
journal = {Groups, geometry, and dynamics},
pages = {91--99},
year = {2023},
volume = {17},
number = {1},
doi = {10.4171/ggd/658},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/658/}
}
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AU - Lei Chen
AU - Kathryn Mann
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JO - Groups, geometry, and dynamics
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