Rigid actions of mapping class groups

Athanase Papadopoulos (1)

1 IRMA - Institut de Recherche Mathématique Avancée

I study various actions of the extended mapping class group of a surface. This includes actions on simplicial complexes and on CW complexes, like the Hatcher-Thurston complex, the Harvey curve complex and various generalizations of these complexes; actions on spaces of measured foliations and of unmeasured foliations; actions on Teichmueller space equipped with various structures; and algebraic actions. The paper grew out of a set of lectures that I gave at the Center for the Topology and Quantization of Muduli spacse (University of Aarhus). A large part of the material presented is expository, but there are also new results. These include results on the action of the extended mapping class group on spaces of foliations, and an outline of recent joint work with John McCarthy on the action of the complex of domains of a surface.

Mots clés: mapping class group; Teichmueller space; Thurston's boundary; measured foliation; unmeasured foliation; curve complex; arc complex; complex of domains; Hatcher-Thurston complex; train track.; train track

Domaines: Topologie géométrique [math.GT]

Athanase Papadopoulos. Rigid actions of mapping class groups. 2007. ⟨hal-00189113⟩