A presentation for the mapping class group of a non-orientable surface from the action on the complex of curves

Details A presentation for the mapping class group of a non-orientable surface from the action on the complex of curves A presentation for the mapping class group of a non-orientable surface from the action on the complex of curves

2007-07-18

arxiv.org/abs/0707.2776v1

Osaka J. Math. 45 (2008), 283-326

Mathematics

Geometric Topology

45 pages, accepted for publication in Osaka J. Math

Scientific paper

We study the action of the mapping class group M(F) on the complex of curves of a non-orientable surface F. We obtain, by using a result of K. S. Brown, a presentation for M(F) defined in terms of the mapping class groups of the complementary surfaces of collections of curves, provided that F is not sporadic, i.e. the complex of curves of F is simply connected. We also compute a finite presentation for the mapping class group of each sporadic surface.

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