Injections of mapping class groups

Details Injections of mapping class groups Injections of mapping class groups

2008-11-05

arxiv.org/abs/0811.0841v1

Mathematics

Geometric Topology

Scientific paper

We construct new monomorphisms between mapping class groups of surfaces. The first family of examples injects the mapping class group of a closed surface into that of a different closed surface. The second family of examples are defined on mapping class groups of once-punctured surfaces and have quite curious behaviour. For instance, some pseudo-Anosov elements are mapped to multi-twists. Neither of these two types of phenomena were previously known to be possible although the constructions are elementary.

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