Mahan Mj (Tata Institute) - Cubulating surface-by-free groups

Graphs, surfaces, and cube complexes
9 July 2018

Abstract: Let 1→H→G→Q→1 be an exact sequence where H=π1(S) is the fundamental group of a closed surface S of genus greater than one, G is hyperbolic and Q is finitely generated free. We shall describe sufficient conditions to prove that G is cubulable. The main result may be thought of as a combination theorem for virtually special hyperbolic groups when the amalgamating subgroup is not quasiconvex. Ingredients include the theory of tracks, the quasiconvex hierarchy theorem of Wise, the distance estimates in the mapping class group from subsurface projections due to Masur-Minsky et al and the model for doubly degenerate Kleinian surface groups used in the proof of the ending lamination theorem.
This is joint work in progress with Jason Manning and Michah Sageev.