4 papers
Planar lattice subsets with minimal vertex boundary
Radhika Gupta, Ivan Levcovitz, Alexander Margolis +1
A subset of vertices of a graph is minimal if, within all subsets of the same size, its vertex boundary is minimal. We give a complete, geometric characterization of minimal sets f…
Subgroups of right-angled Coxeter groups via Stallings-like techniques
Pallavi Dani, Ivan Levcovitz
We associate cube complexes called completions to each subgroup of a right-angled Coxeter group (RACG). A completion characterizes many properties of the subgroup such as whether i…
Comparing the Roller and B(X) boundaries of CAT(0) cube complexes
Ivan Levcovitz
The Roller boundary is a well-known compactification of a CAT(0) cube complex X. When X is locally finite, essential, irreducible, non-Euclidean and admits a cocompact action by a…
Thick groups have trivial Floyd boundary
Ivan Levcovitz
We prove that thick groups (and more generally thick graphs) have trivial Floyd boundary. This shows a wide class of finitely generated groups that are non-relatively hyperbolic ha…