Event
Mark Hagen, University of Bristol
Wednesday, January 31, 2018 15:00to16:00
Burnside Hall
Room 920, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA
Extremal panels and taco moves.
There are various interesting statements that boil down to passing from an action of a group G on a CAT(0) cube complex to an action on a tree. These include Stallings' ends theorem, the Nielsen realisation theorem for Out(F_n), and the Kropholler-Roller conjecture about almost-invariant subsets. I will discuss a method for converting a G-action on a CAT(0) cube complex X to a G-action on a "lower complexity" CAT(0) cube complex Y and describe conditions under which this can be used inductively to find a splitting of G. This leads to new proofs of the first two of the preceding statements, as well as a special case of the Kropholler-Roller conjecture. I will also briefly describe some possible generalisations of the construction. Most of this talk is on joint work with Nicholas Touikan; it will also touch on some joint work with Henry Wilton.