24 citations · 178 across the 25 of their papers we have counts for
26 papers
Hyperbolic models and stability recognition for Coxeter groups
Christopher H. Cashen, Michelle Chu, Jing Tao
Given a finite rank Coxeter system, we construct a hyperbolic space by coning off the wide parabolic subcomplexes of its Davis complex. The resulting space is ``stability recognizi…
Biggs tree groups
Christopher H. Cashen
Biggs gave an explicit construction, using finite colored trees, of finite permutation groups whose Cayley graphs have valence \(C\) and girth tending to infinity as the radius \(R…
Conformal dimension bounds, Pontryagin sphere boundaries, and algebraic fibering of right-angled Coxeter groups
Christopher H. Cashen, Pallavi Dani, Kevin Schreve +1
We introduce a graph-theoretic condition, called --branching, that ensures a combinatorial round tree with controlled branching parameters can be quasi-isometrically embedde…
RAAGedy right-angled Coxeter groups
Christopher H. Cashen, Pallavi Dani, Alexandra Edletzberger +1
We give criteria for deciding whether or not a triangle-free simple graph is the presentation graph of a right-angled Coxeter group that is quasiisometric to some right-angled Arti…
RAAGedy right-angled Coxeter groups II: in the quasiisometry class of the tree RAAGs
Christopher H. Cashen
We classify two-dimensional right-angled Coxeter groups that are quasiisometric to a right-angled Artin group defined by a tree, and show that when this is true the right-angled Co…
Visual right-angled Artin subgroups of two-dimensional right-angled Coxeter groups
Christopher H. Cashen, Alexandra Edletzberger
There is a procedure, due to Dani and Levcovitz, for taking a finite simplicial graph (Γ) and a subgraph (Λ) of its complement, checking some conditions, and, if satisfied, produci…
GAGTA 2023 Problem Session
Henry Bradford, Christopher H. Cashen, Francesco Fournier-Facio +2
The conference `Geometric and Asymptotic Group Theory with Applications (GAGTA) 2023: Groups and Dynamics' took place at the Erwin Schrödinger Institute on July 17-21. These are th…
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…
Short, highly imprimitive words yield hyperbolic one-relator groups
Christopher H. Cashen, Charlotte Hoffmann
We give experimental support for a conjecture of Louder and Wilton saying that words of imprimitivity rank greater than two yield hyperbolic one-relator groups.
Morse subsets of CAT(0) spaces are strongly contracting
Christopher H. Cashen
We prove that Morse subsets of CAT(0) spaces are strongly contracting. This generalizes and simplifies a result of Sultan, who proved it for Morse quasi-geodesics. Our proof goes t…
Cogrowth for group actions with strongly contracting elements
Goulnara N. Arzhantseva, Christopher H. Cashen
Let be a group acting properly by isometries and with a strongly contracting element on a geodesic metric space. Let be an infinite normal subgroup of , and let an…
A Metrizable Topology on the Contracting Boundary of a Group
Christopher H. Cashen, John M. Mackay
The 'contracting boundary' of a proper geodesic metric space consists of equivalence classes of geodesic rays that behave like rays in a hyperbolic space. We introduce a geometrica…
Quasi-isometries need not induce homeomorphisms of contracting boundaries with the Gromov product topology
Christopher H. Cashen
We consider a `contracting boundary' of a proper geodesic metric space consisting of equivalence classes of geodesic rays that behave like geodesics in a hyperbolic space. We topol…
Negative curvature in graphical small cancellation groups
Goulnara N. Arzhantseva, Christopher H. Cashen, Dominik Gruber +1
We use the interplay between combinatorial and coarse geometric versions of negative curvature to investigate the geometry of infinitely presented graphical small cancel…
Quasi-isometries Between Groups with Two-Ended Splittings
Christopher H. Cashen, Alexandre Martin
We construct `structure invariants' of a one-ended, finitely presented group that describe the way in which the factors of its JSJ decomposition over two-ended subgroups fit togeth…
Characterizations of Morse quasi-geodesics via superlinear divergence and sublinear contraction
Goulnara N. Arzhantseva, Christopher H. Cashen, Dominik Gruber +1
We introduce and begin a systematic study of sublinearly contracting projections. We give two characterizations of Morse quasi-geodesics in an arbitrary geodesic metric space. One…
Mapping tori of free group automorphisms, and the Bieri-Neumann-Strebel invariant of graphs of groups
Christopher H. Cashen, Gilbert Levitt
Let be the mapping torus of a polynomially growing automorphism of a finitely generated free group. We determine which epimorphisms from to have finitely gener…
Virtual Geometricity is Rare
Christopher H. Cashen, Jason F. Manning
We present the results of computer experiments suggesting that the probability that a random multiword in a free group is virtually geometric decays to zero exponentially quickly i…
Growth Tight Actions of Product Groups
Christopher H. Cashen, Jing Tao
A group action on a metric space is called growth tight if the exponential growth rate of the group with respect to the induced pseudo-metric is strictly greater than that of its q…
Quasi-isometry Invariants from Decorated Trees of Cylinders of Two-Ended JSJ Decompositions
Christopher H. Cashen
We construct quasi-isometry invariants of a one-ended finitely presented group by considering the tree of cylinders of a two-ended JSJ decomposition of the group. When the group sa…
Growth Tight Actions
Goulnara N. Arzhantseva, Christopher H. Cashen, Jing Tao
We introduce and systematically study the concept of a growth tight action. This generalizes growth tightness for word metrics as initiated by Grigorchuk and de la Harpe. Given a f…
A Geometric Proof of the Structure Theorem for Cyclic Splittings of Free Groups
Christopher H. Cashen
We give a geometric proof of a well known theorem that describes splittings of a free group as an amalgamated product or HNN extension over the integers. The argument generalizes t…
Splitting Line Patterns in Free Groups
Christopher H. Cashen
We construct a boundary of a finite rank free group relative to a finite list of conjugacy classes of maximal cyclic subgroups. From the cut points and uncrossed cut pairs of this…
Line Patterns in Free Groups
Christopher H. Cashen, Natasa Macura
We study line patterns in a free group by considering the topology of the decomposition space, a quotient of the boundary at infinity of the free group related to the line pattern.…