16 citations · 52 across the 11 of their papers we have counts for
11 papers
Two conjectures on coarse conjugacy by Geller and Misiurewicz
Damian Sawicki
In their study of coarse entropy, W. Geller and M. Misiurewicz introduced the notion of coarse conjugacy: a version of conjugacy appropriate for dynamics on metric spaces observed…
Spectral gap and origami expanders
Goulnara Arzhantseva, Dawid Kielak, Tim de Laat +1
We construct the first measure-preserving affine actions with spectral gap on surfaces of arbitrary genus . We achieve this by finding geometric representatives of multi-twi…
Coarse entropy of metric spaces
William Geller, Michał Misiurewicz, Damian Sawicki
Coarse geometry studies metric spaces on the large scale. The recently introduced notion of coarse entropy is a tool to study dynamics from the coarse point of view. We prove that…
Dynamic asymptotic dimension for actions of virtually cyclic groups
Massoud Amini, Kang Li, Damian Sawicki +1
We show that the dynamic asymptotic dimension of a minimal free action of an infinite virtually cyclic group on a compact Hausdorff space is always one. This extends a well-known r…
Warped cones, (non-)rigidity, and piecewise properties, with a joint appendix with Dawid Kielak
Damian Sawicki
We prove that if a quasi-isometry of warped cones is induced by a map between the base spaces of the cones, the actions must be conjugate by this map. The converse is false in gene…
Straightening warped cones
Damian Sawicki, Jianchao Wu
We provide the converses to two results of J. Roe (Geom. Topol. 2005): first, the warped cone associated to a free action of an a-T-menable group admits a fibred coarse embedding i…
Super-expanders and warped cones
Damian Sawicki
For a Banach space , we show that any family of graphs quasi-isometric to levels of a warped cone is an expander with respect to if and only if the induced $…
Warped cones and spectral gaps
Piotr W. Nowak, Damian Sawicki
We show that warped cones over actions with spectral gaps do not embed coarsely into large classes of Banach spaces. In particular, there exist warped cones over actions of the fre…
Warped cones over profinite completions
Damian Sawicki
We construct metric spaces that do not have property A yet are coarsely embeddable into the Hilbert space. Our examples are so called warped cones, which were introduced by J. Roe…
On equivariant asymptotic dimension
Damian Sawicki
The work discusses equivariant asymptotic dimension (also known as "wide equivariant covers", "--amenability" or "amenability dimension", and "-BLR condition") an…
Remarks on coarse triviality of asymptotic Assouad-Nagata dimension
Damian Sawicki
We show for a given metric space of asymptotic dimension that there exists a coarsely and topologically equivalent hyperbolic metric of the form s…