Homology and dynamics in quasi-isometric rigidity of once-punctured mapping class groups

Details Homology and dynamics in quasi-isometric rigidity of once-punctured mapping class groups Homology and dynamics in quasi-isometric rigidity of once-punctured mapping class groups

2003-08-07

arxiv.org/abs/math/0308065v1

Mathematics

Group Theory

Lecture Notes from the LMS Durham Symposium: Geometry and Cohomology in Group Theory, University of Durham, UK, July 2003

Scientific paper

In these lecture notes, we combine recent homological methods of Kevin Whyte with older dynamical methods developed by Benson Farb and myself, to obtain a new quasi-isometric rigidity theorem for the mapping class group MCG(S) of a once punctured surface S of genus at least 2: if K is a finitely generated group quasi-isometric to MCG(S) then there is a homomorphism K -> MCG(S) with finite kernel and finite index image. This theorem is joint with Kevin Whyte.

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