School of Mathematics & Physics, University of Lincoln
Abstract: Thompson’s group V is probably one of the best known examples of a finitely presented infinite simple group. The presentation originally given by Thompson in his notes has remained the best in terms of fewest generators and relations until very recently. I will present recent work with Collin Bleak that gives new presentations for V including one involving fewer relations than Thompson’s presentation. There are a number of other infinite simple groups that arise as generalisations of Thompson’s group V. One set of examples are the groups nV (for positive integers n) introduced by Brin and that act upon n-dimensional Cantor space. I will present ongoing work that produces presentations for the groups nV and that draws attention to the interaction between the baker’s maps on n-dimensional Cantor space and transpositions of basic open sets.