The Geometry of Finitely Presented Infinite Simple Groups

Abstract

Let g be the family of finitely presented infinite simple groups introducedby Higman,generalizing R.J. Thompson’s group of dyadic home! omorphisms of the Cantor set. For each G E g and each integer n 2 1, an (n " 1)-connected n"dimensional simplicial complex is constructed, on which G acts with finite stabilizers and with an n"simplex as fundamen! tal domain. This yields homologicaland combinatorial information about G. As a by"product, one obtains a solution to a problem of Neumann and Neumann.