Groups and Dynamics Seminar

Date: September 9, 2015

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Volodymyr Nekrashevych, Texas A&M University

Title: On full groups of etale groupoids

Abstract: Topological full groups of etale groupoids are natural generalizations of topological full groups of homeomorphisms (as defined by Giordano, Putnam, and Skau). H. Matui showed for some special classes of groupoids that the derived subgroup of the topological full group is simple and finitely generated. We introduce a special subgroup A(G) of the full group [[G]] of an etale groupoid G, and show that for all minimal groupoids the group A(G) is simple and is contained in every non-trivial normal subgroup of the full group. We also show that if G is expansive (e.g., the groupoid of an expansive action of a finitely generated group) then A(G) is finitely generated. For the groupoids studied by H. Matui the group A(G) coincides with the dervied subgroup of the full group.