There are no exotic actions of diffeomorphism groups on 1-manifolds
Lei Chen
University of Maryland, College Park, USAKathryn Mann
Cornell University, Ithaca, USA
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Abstract
Let be a manifold and a -dimensional manifold. Assuming that , we show that any nontrivial homomorphism has a standard form: necessarily is -dimensional, and there are countably many embeddings with disjoint images such that the action of is conjugate (via the product of the ) to the diagonal action of on on , and trivial elsewhere. This solves a conjecture of Matsumoto. We also show that the groups have no countable index subgroups.
Cite this article
Lei Chen, Kathryn Mann, There are no exotic actions of diffeomorphism groups on 1-manifolds. Groups Geom. Dyn. 17 (2023), no. 1, pp. 91–99
DOI 10.4171/GGD/658