4 citations · 15 across the 11 of their papers we have counts for
11 papers
Common overlattices in trees and trees with fins
Sam Shepherd
Bass and Kulkarni proved that any pair of free uniform lattices in the automorphism group of a tree have conjugates that both lie inside a third uniform lattice (which is not neces…
Splittings of One-Ended Groups with One-Ended Halfspaces
Michael Mihalik, Sam Shepherd
We introduce the notion of halfspaces associated to a group splitting, and investigate the relationship between the coarse geometry of the halfspaces and the coarse geometry of the…
Graphically discrete groups and rigidity
Alex Margolis, Sam Shepherd, Emily Stark +1
We introduce the notion of graphical discreteness to group theory. A finitely generated group is graphically discrete if whenever it acts geometrically on a locally finite graph, t…
A cubulation with no factor system
Sam Shepherd
The primary method for showing that a given cubulated group is hierarchically hyperbolic is by constructing a factor system on the cube complex. In this paper we show that such a c…
Semistability of cubulated groups
Sam Shepherd
We prove that all cubulated groups are semistable at infinity. In doing so we prove two further results about cubulations of groups. The first of these states that any one-ended cu…
Commensurability of lattices in right-angled buildings
Sam Shepherd
Let be a graph product of finite groups, with finite underlying graph, and let be the associated right-angled building. We prove that a uniform lattice in the cubical a…
Imitator homomorphisms for special cube complexes
Sam Shepherd
Central to the theory of special cube complexes is Haglund and Wise's construction of the canonical completion and retraction, which enables one to build finite covers of special c…
Leighton's Theorem: extensions, limitations, and quasitrees
Martin R. Bridson, Sam Shepherd
Leighton's Theorem states that if there is a tree that covers two finite graphs and , then there is a finite graph that is covered by and covers both $G…
Quasi-isometric rigidity for graphs of virtually free groups with two-ended edge groups
Sam Shepherd, Daniel J. Woodhouse
We study the quasi-isometric rigidity of a large family of finitely generated groups that split as graphs of groups with virtually free vertex groups and two-ended edge groups. Let…
Two generalisations of Leighton's Theorem
Sam Shepherd, Giles Gardam, Daniel J. Woodhouse
Leighton's graph covering theorem says that two finite graphs with a common cover have a common finite cover. We present a new proof of this using groupoids, and use this as a mode…
Agol's theorem on hyperbolic cubulations
Sam Shepherd
Agol proved that hyperbolic cubulated groups are virtually special. The aim of these notes is to make the proof accessible to a wider audience; we retain the underlying ideas and c…