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Homomorphisms between mapping class groups

Aramayona, Javier
; 
Souto, Juan
Identifiers
http://hdl.handle.net/10379/10276
 https://doi.org/10.13025/27489
Publication Date
2012-12-31
Keywords
compact riemann surfaces, automorphism-groups, orientable surface, subgroups, homeomorphisms, realization, curves
Type
Article
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Citation
Aramayona, Javier; Souto, Juan (2012). Homomorphisms between mapping class groups. Geometry & Topology 16 (4), 2285-2341
Abstract
Suppose that X and Y are surfaces of finite topological type, where X has genus g >= 6 and Y has genus at most 2g - 1; in addition, suppose that Y is not closed if it has genus 2g - 1. Our main result asserts that every nontrivial homomorphism Map(X ) -> Map(Y) is induced by an embedding, ie a combination of forgetting punctures, deleting boundary components and subsurface embeddings. In particular, if X has no boundary then every nontrivial endomorphism Map(X) -> Map(X) is in fact an isomorphism.
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Publisher
Mathematical Sciences Publishers
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Externally hosted open access publications with University of Galway authors (2)