Event № 676
A group G is called bounded if every biinvariant metric on G has finite diameter. If G is generated by finitely many conjugacy classes then G is bounded if every biinvariant word metric has finite diameter. In this case the diameter (of course) depends on the choice of a generating set and this is where things become subtle. I will discuss these subtleties (examples: SL(n,Z), some cocompact lattices, Ham(M,w)) and present applications to finite simple groups and Hamiltonian group actions on symplectic manifolds (example: the automorphism group of a regular tree of valence at least three does not admit a faithful Hamiltonian action on a closed symplectic manifold).
Joint work with Assaf Libman and Ben Martin.