The Shapes of Books: Hadas, Kaminsky, Dawson, Stallings

The William Stallings Books on Computer

Open Books Supporting Overtwisted Contact Structures and Stallings Twist

We study open books (or open book decompositions) of a closed oriented 3-manifold which support overtwisted contact structures. We focus on a simple closed curve along which one can perform Stallings twist, called “twisting loop”. We show that the existence of a twisting loop on the fiber surface of an open book is equivalent up to positive stabilization to the existence of an overtwisted disk ...

On Stallings Fibrations

The Dehn function of Stallings’ group

We prove that the Dehn function of a group of Stallings that is finitely presented but not of type F3 is quadratic.

Stallings’ folds for cube complexes

We describe a higher dimensional analogue of Stallings’ folding sequences for group actions on CAT(0) cube complexes. We use it to give a characterization of quasiconvex subgroups of hyperbolic groups that act properly co-compactly on CAT(0) cube complexes via finiteness properties of their hyperplane stabilizers.