Strong boundedness and distortion in transformation groups
Amenability, coarse embeddability and fixed point properties December 06, 2016  December 09, 2016
Location: SLMath: Eisenbud Auditorium
strong distortion
diffeomorphism groups
transformation groups
homeomorphism
Amenability
aTmenability
fixed point properties
hyperbolic groups and generalizations
Banach space
group cohomology
expander graph
index theory
noncommutative geometry
00A35  Methodology of mathematics {For mathematics education, see 97XX}
00B25  Proceedings of conferences of miscellaneous specific interest
00B55  Collections of translated articles of miscellaneous specific interest
0111  Research data for problems pertaining to history and biography
20E15  Chains and lattices of subgroups, subnormal subgroups [See also 20F22]
14649
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
Mann Notes

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