49 citations · 218 across the 20 of their papers we have counts for
20 papers
Asymptotic dimension for covers with controlled growth
David Hume, John M. Mackay, Romain Tessera
We prove various obstructions to the existence of regular maps (or coarse embeddings) between commonly studied spaces. For instance, there is no regular map (or coarse embedding) $…
Maps between relatively hyperbolic spaces and between their boundaries
John M. Mackay, Alessandro Sisto
We study relations between maps between relatively hyperbolic groups/spaces and quasisymmetric embeddings between their boundaries. More specifically, we establish a correspondence…
Poincaré profiles of Lie groups and a coarse geometric dichotomy
David Hume, John M. Mackay, Romain Tessera
Poincaré profiles are a family of analytically defined coarse invariants, which can be used as obstructions to the existence of coarse embeddings between metric spaces. In this pap…
Conformal dimension of hyperbolic groups that split over elementary subgroups
Matias Carrasco, John M. Mackay
We study the (Ahlfors regular) conformal dimension of the boundary at infinity of Gromov hyperbolic groups which split over elementary subgroups. If such a group is not virtually f…
Poorly connected groups
David Hume, John M. Mackay
We investigate groups whose Cayley graphs have poor\-ly connected subgraphs. We prove that a finitely generated group has bounded separation in the sense of Benjamini--Schramm--Tim…
Random triangular Burnside groups
Dominik Gruber, John M. Mackay
We introduce a model for random groups in varieties of -periodic groups as -periodic quotients of triangular random groups. We show that for an explicit $d_{\mathrm{crit}}\in…
Poincaré profiles of groups and spaces
David Hume, John M. Mackay, Romain Tessera
We introduce a spectrum of monotone coarse invariants for metric measure spaces called Poincaré profiles. The two extremes of this spectrum determine the growth of the space, and t…
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…
Random groups, random graphs and eigenvalues of p-Laplacians
Cornelia Drutu, John M. Mackay
We prove that a random group in the triangular density model has, for density larger than 1/3, fixed point properties for actions on -spaces (affine isometric, and more genera…
A sharper threshold for random groups at density one-half
Moon Duchin, Kasia Jankiewicz, Shelby C. Kilmer +3
In the density model of random groups, we consider presentations with any fixed number m of generators and many random relators of length l, sending l to infinity. If d is a "densi…
Conformal dimension via subcomplexes for small cancellation and random groups
John M. Mackay
We find new bounds on the conformal dimension of small cancellation groups. These are used to show that a random few relator group has conformal dimension 2+o(1) asymptotically alm…
Balanced walls for random groups
John M. Mackay, Piotr Przytycki
We study a random group G in the Gromov density model and its Cayley complex X. For density < 5/24 we define walls in X that give rise to a nontrivial action of G on a CAT(0) cube…
Quasi-circles through prescribed points
John M. Mackay
We show that in an L-annularly linearly connected, N-doubling, complete metric space, any n points lie on a K-quasi-circle, where K depends only on L, N and n. This implies, for ex…
Embedding relatively hyperbolic groups in products of trees
John M. Mackay, Alessandro Sisto
We show that a relatively hyperbolic group quasi-isometrically embeds in a product of finitely many trees if the peripheral subgroups do, and we provide an estimate on the minimal…
Modulus and Poincaré inequalities on non-self-similar Sierpinski carpets
John M. Mackay, Jeremy T. Tyson, Kevin Wildrick
A carpet is a metric space homeomorphic to the Sierpinski carpet. We characterize, within a certain class of examples, non-self-similar carpets supporting curve families of nontriv…
Quasi-hyperbolic planes in relatively hyperbolic groups
John M. Mackay, Alessandro Sisto
We show that any group that is hyperbolic relative to virtually nilpotent subgroups, and does not admit peripheral splittings, contains a quasi-isometrically embedded copy of the h…
Conformal dimension and random groups
John M. Mackay
We give a lower and an upper bound for the conformal dimension of the boundaries of certain small cancellation groups. We apply these bounds to the few relator and density models f…
Assouad dimension of self-affine carpets
John M. Mackay
We calculate the Assouad dimension of the self-affine carpets of Bedford and McMullen, and of Lalley and Gatzouras. We also calculate the conformal Assouad dimension of those carpe…
Spaces and groups with conformal dimension greater than one
John M. Mackay
We show that if a complete, doubling metric space is annularly linearly connected then its conformal dimension is greater than one, quantitatively. As a consequence, we answer a qu…
Existence of quasi-arcs
John M. Mackay
We show that doubling, linearly connected metric spaces are quasi-arc connected. This gives a new and short proof of a theorem of Tukia.