Abstract
Suppose that and are surfaces of finite topological type, where has genus and has genus at most ; in addition, suppose that is not closed if it has genus . Our main result asserts that every nontrivial homomorphism is induced by an embedding, ie a combination of forgetting punctures, deleting boundary components and subsurface embeddings. In particular, if has no boundary then every nontrivial endomorphism is in fact an isomorphism.
Citation
Javier Aramayona. Juan Souto. "Homomorphisms between mapping class groups." Geom. Topol. 16 (4) 2285 - 2341, 2012. https://doi.org/10.2140/gt.2012.16.2285
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