MATH 7570 - Topics in Topology: Cubulating Spaces and Groups

Jason Manning, fall 2014.

Recent work of Agol and Wise resolved several important conjectures in group theory and topology, including the virtual haken conjecture for three-manifolds. A key idea (due to Sageev) is the "cubulation" of groups using codimension one subgroups. Haglund and Wise related "special" cubulations to topological lifting problems and profinite qualities of groups. We'll give several characterizations of these "special" cubulations and build up as much of the Agol-Wise theory as time allows.