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Three proofs from dynamics of rigidity of surface group actions

Dynamics on Moduli Spaces April 13, 2015 - April 17, 2015

April 15, 2015 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Kathryn Mann (University of California, Berkeley)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • surface group

  • rigidity results

  • discrete subgroups

  • folations - leaves

  • Hitchin representation

  • geometric actions

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14221

Abstract

In previous talks (not a prerequisite!), I've described examples of actions of a surface group G on the circle that are totally rigid -- they are essentially isolated points in the representation space Hom(G, Homeo+(S^1))/~.   These examples are interesting from many perspectives, ranging from foliation theory to the classification of connected components of representation spaces.    

 

In this talk, I will illustrate three separate approaches to prove rigidity of these actions, including my original proof.   Each one uses fundamentally different techniques, but all have a common dynamical flavor:

1. Structural stability of Anosov foliations (Ghys/Bowden, under extra hypotheses)

2. Rotation number "trace coordinates" on the representation space (Mann)

3. New "ping-pong" lemmas for surface groups (Matsumoto)

 

Supplements
23393?type=thumb Mann.Notes 479 KB application/pdf Download
Video/Audio Files

14221

H.264 Video 14221.mp4 363 MB video/mp4 rtsp://videos.msri.org/data/000/023/286/original/14221.mp4 Download
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