1 citations · 5 across the 7 of their papers we have counts for
11 papers
Hex implies Y
Tomasz Prytuła
We give a simple and short proof of the fact that the board game of Y cannot end in a draw. Our proof, based on the analogous result for the game of Hex (the so-called 'Hex Theorem…
Cohomological and geometric invariants of simple complexes of groups
Nansen Petrosyan, Tomasz Prytuła
We investigate strictly developable simple complexes of groups with arbitrary local groups, or equivalently, group actions admitting a strict fundamental domain. We introduce a new…
Graphical complexes of groups
Tomasz Prytuła
We introduce graphical complexes of groups, which can be thought of as a generalisation of Coxeter systems with 1-dimensional nerves. We show that these complexes are strictly deve…
Coarse geometry of the fire retaining property and group splittings
Eduardo Martínez-Pedroza, Tomasz Prytuła
Given a non-decreasing function we define a single player game on (infinite) connected graphs that we call fire retaining. If a graph admit…
Commensurators of abelian subgroups in CAT(0) groups
Jingyin Huang, Tomasz Prytuła
We study the structure of the commensurator of a virtually abelian subgroup in , where acts properly on a space . When is a Hadamard manifold an…
Bredon cohomological dimension for virtually abelian stabilisers for CAT(0) groups
Tomasz Prytuła
Given a discrete group , for any integer we consider the family of all virtually abelian subgroups of of rank at most . We give an upper bound for the Bredo…
Bestvina complex for group actions with a strict fundamental domain
Nansen Petrosyan, Tomasz Prytuła
We consider a strictly developable simple complex of finite groups . We show that Bestvina's construction for Coxeter groups applies in this more general setting to…
Solvable Subgroup Theorem for simplicial nonpositive curvature
Tomasz Prytuła
Given a group with bounded torsion that acts properly on a systolic complex, we show that every solvable subgroup of is finitely generated and virtually abelian of rank at…
Hyperbolic isometries and boundaries of systolic complexes
Tomasz Prytuła
Given a group acting geometrically on a systolic complex and a hyperbolic isometry , we study the associated action of on the systolic boundary . W…
Classifying spaces for families of subgroups for systolic groups
Damian Osajda, Tomasz Prytuła
We determine the large scale geometry of the minimal displacement set of a hyperbolic isometry of a systolic complex. As a consequence, we describe the centraliser of such an isome…
Infinite systolic groups are not torsion
Tomasz Prytuła
We study -systolic complexes introduced by T. Januszkiewicz and J. Świątkowski, which are simply connected simplicial complexes of simplicial nonpositive curvature. Using techni…