16 citations · 38 across the 11 of their papers we have counts for
16 papers
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…
Asymptotic cones of snowflake groups and the strong shortcut property
Christopher H. Cashen, Nima Hoda, Daniel J. Woodhouse
We exhibit an infinite family of snowflake groups all of whose asymptotic cones are simply connected. Our groups have neither polynomial growth nor quadratic Dehn function, the two…
Leighton's Theorem and Regular Cube Complexes
Daniel J. Woodhouse
Leighton's graph covering theorem states that two finite graphs with common universal cover have a common finite cover. We generalize this to a large family of non-positively curve…
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…
Action rigidity for free products of hyperbolic manifold groups
Emily Stark, Daniel J. Woodhouse
Two groups have a common model geometry if they act properly and cocompactly by isometries on the same proper geodesic metric space. The Milnor-Schwarz lemma implies that groups wi…
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…
Hyperbolic groups that are not commensurably coHopfian
Emily Stark, Daniel J. Woodhouse
Sela proved every torsion-free one-ended hyperbolic group is coHopfian. We prove that there exist torsion-free one-ended hyperbolic groups that are not commensurably coHopfian. In…
Residually Finite Tubular Groups
Nima Hoda, Daniel T. Wise, Daniel J. Woodhouse
A tubular group is a finite graph of groups with vertex groups and edge groups. We characterize residually finite tubular groups: is residually…
Revisiting Leighton's Theorem with the Haar Measure
Daniel J. Woodhouse
Leighton's graph covering theorem states that a pair of finite graphs with isomorphic universal covers have a common finite cover. We provide a new proof of Leighton's theorem that…
The geometry of one-relator groups satisfying a polynomial isoperimetric inequality
Giles Gardam, Daniel J. Woodhouse
For every pair of positive integers we construct a one-relator group whose Dehn function is where . The group has no…
Quasi-isometric groups with no common model geometry
Emily Stark, Daniel Woodhouse
A simple surface amalgam is the union of a finite collection of surfaces with precisely one boundary component each and which have their boundary curves identified. We prove if two…
Classifying Virtually Special Tubular Groups
Daniel J. Woodhouse
A group is tubular if it acts on a tree with vertex stabilizers and edge stabilizers. We prove that a tubular group is virtually special if and only if…
A Generalized Axis Theorem for Cube Complexes
Daniel J. Woodhouse
We consider a finitely generated virtually abelian group acting properly and without inversions on a CAT(0) cube complex . We prove that stabilizes a finite dimensional…
ATmenability of some graphs of groups with cyclic edge groups
Mathieu Carette, Daniel T. Wise, Daniel J. Woodhouse
We show that certain graphs of groups with cyclic edge groups are aTmenable. In particular, this holds when each vertex group is either virtually special or acts properly and semis…
A Cubical Flat Torus Theorem and the Bounded Packing Property
Daniel T. Wise, Daniel J. Woodhouse
We prove the bounded packing property for any abelian subgroup of a group acting properly and cocompactly on a CAT(0) cube complex. A main ingredient of the proof is a cubical flat…
Classifying Finite Dimensional Cubulations of Tubular Groups
Daniel J. Woodhouse
A tubular group is a group that acts on a tree with vertex stabilizers and edge stabilizers. This paper develops further a criterion of Wise and determi…