5 papers
Constructing metric spaces from systems of walls
Harry Petyt, Abdul Zalloum, Davide Spriano
We give a general procedure for constructing metric spaces from systems of partitions. This generalises and provides analogues of Sageev's construction of dual CAT(0) cube complexe…
Pseudo-Anosov flows and the geometry of Anosov-like group actions
Thomas Barthelmé, Kathryn Mann, Neige Paulet +1
We show that the action on its orbit space induced by a pseudo-Anosov flow on a closed -manifold (and more general Anosov-like actions) can be seen as an isometric action on a G…
Growth tightness and genericity for word metrics from injective spaces
Lihuang Ding, DÃdac MartÃnez-Granado, Abdul Zalloum
Mapping class groups are known to admit geometric (proper, cobounded) actions on injective spaces. Starting with such an action, and relying only on geometric arguments, we show th…
Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups
Carolyn Abbott, Mark Hagen, Harry Petyt +1
We show that infinite cyclic subgroups of groups acting uniformly properly on injective metric spaces are uniformly undistorted. In the special case of hierarchically hyperbolic gr…
Stable cylinders and fine structures for hyperbolic groups and curve graphs
Harry Petyt, Davide Spriano, Abdul Zalloum
In 1995, Rips and Sela asked if torsionfree hyperbolic groups admit globally stable cylinders. We establish this property for all residually finite hyperbolic groups and curve grap…