Montreal Geometric & Combinatorial Group Theory Seminar

 

 

Speaker: Tim Hsu (San Jose State)

Title: "Groups with infinitely many types of fixed subgroups"

Date: 3:30pm Wednesday, March 26th.

Room: 920 Burnside

 

Abstract:

 

It is a theorem of Bestvina and Handel that if f is an

automorphism of a rank r free group G then the rank of FIX(f) is <= r.

Note that Fix(f) is the subgroup consisting of elements g s.t. f(g)=g.

More generally, Shore has shown that if G is word-hyperbolic, then up to isomorphism, only finitely many groups appear as fixed subgroups of automorphisms of G.  We show that if the negative curvature condition in Shore's result is relaxed to a nonpositive curvature condition, then the result no longer holds.  Specifically, we give an example of a group G that acts properly and cocompactly on a CAT(0) space such that infinitely many non-isomorphic groups appear as fixed subgroups of automorphisms of G.