1 citations · 3 across the 9 of their papers we have counts for
10 papers
Cubical small-cancellation quotients of non-products
Macarena Arenas, Kasia Jankiewicz, Daniel T. Wise
We show that if is a compact nonpositively curved cube complex which is a non-product, then has a proper quotient that is of a cube complex with these same proper…
Asphericity of cubical presentations: the general case
Macarena Arenas
We show that, under suitable hypotheses, the coned-off spaces associated to cubical small-cancellation presentations are aspherical, and use this to provide classifying spac…
Taut smoothings of arcs and curves
Macarena Arenas, Max Neumann-Coto
We study the geometric and combinatorial effect of smoothing an intersection point in a collection of arcs or curves on a surface. We prove that all taut arcs with fixed endpoints…
Grupos y geometría cubular
Macarena Arenas
This survey paper, written in spanish, is an extended version of lecture notes for a mini-course taught at the 2022 Summer School in Geometric Group Theory, which took place in the…
The Cohen--Lyndon property in non-metric small-cancellation
Macarena Arenas, Karol Duda
We show that the Cohen--Lyndon property holds for all non-metric small-cancellation quotients. This generalises the analogous result from the metric small-cancellation setting, and…
Hyperbolicity in non-metric cubical small-cancellation
Macarena Arenas, Kasia Jankiewicz, Daniel T. Wise
Given a non-positively curved cube complex , we prove that the quotient of defined by a cubical presentation satisfying sufficient n…
Asphericity of cubical presentations: the 2-dimensional case
Macarena Arenas
We show that under suitable hypotheses, the second homotopy group of the coned-off space associated to a cubical presentation is trivial, and use this to provide classifying…
Linear isoperimetric functions for surfaces in hyperbolic groups
Macarena Arenas, Daniel T. Wise
We show that word-hyperbolic groups satisfy linear isoperimetric functions for all homotopy types of surface diagrams. This generalises the linear isoperimetric functions for disc…
A cubical Rips construction
Macarena Arenas
Given a finitely presented group and a compact special cube complex with non-elementary hyperbolic fundamental group, we produce a non-elementary, torsion-free, cocompactly…
Measuring complexity of curves on surfaces
Max Neumann-Coto, Macarena Covadonga Robles Arenas
We consider the relations between different measures of complexity for free homotopy classes of curves on a surface , including the minimum number of self-intersections, the min…