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Strong boundedness and distortion in transformation groups

Amenability, coarse embeddability and fixed point properties December 06, 2016 - December 09, 2016

December 08, 2016 (03:30 PM PST - 04:30 PM PST)
Speaker(s): Kathryn Mann (Cornell University)
Location: MSRI: Simons Auditorium
  • strong distortion

  • diffeomorphism groups

  • transformation groups

  • homeomorphism

  • Amenability

  • a-T-menability

  • fixed point properties

  • hyperbolic groups and generalizations

  • Banach space

  • group cohomology

  • expander graph

  • index theory

  • non-commutative geometry

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



Higman’s embedding theorem says that any countable group can be embedded in a group generated by two elements. The relative version of this asks: given a countable subgroup H of a large group G, does H always lie in a finitely generated subgroup of G? (Of course, the answer should depend on G). This talk will answer this question for some interesting classes of groups, and discuss the related notions of strong boundedness (the property that every action of G by isometries on any metric space has all orbits bounded) and strong distortion. Far from pathological examples, the groups we consider are all groups of homeomorphisms or diffeormophisms of manifolds; where boundedness and distortion of subgroups of homeomorphisms can say something about the dynamics of their actions on the manifold. This is new joint work with F. Le Roux

27477?type=thumb Mann Notes 1.61 MB application/pdf Download
Video/Audio Files


H.264 Video 14649.mp4 338 MB video/mp4 rtsp://videos.msri.org/data/000/027/248/original/14649.mp4 Download
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