Publications (10)
Characterizing property (NL) in {C}oxeter groups
Sahana Balasubramanya, Rachel Niebler, Roberta Shapiro
A group has Property (NL) -- which stands for ``no loxodromics" -- if no element of the group acts loxodromically on any hyperbolic space. In this brief note, we provide a complete…
Automorphisms of the k-curve graph
Shuchi Agrawal, Tarik Aougab, Yassin Chandran +4
Given a natural number k and an orientable surface S of finite type, define the k-curve graph to be the graph with vertices corresponding to isotopy classes of essential simple clo…
An Alexander method for infinite-type surfaces
Roberta Shapiro
The Alexander method is a combinatorial tool used to determine when two elements of the mapping class group are equal. We extend the Alexander method to include the case of infinit…
Automorphisms of fine curve graphs of planar surfaces
Roberta Shapiro, Rohan Wadhwa, Arthur Wang +1
The fine curve graph of a surface is the graph whose vertices are simple closed essential curves in the surface and whose edges connect disjoint curves. In this paper, we prove tha…
A challenger to elliptic billiards fails: String construction over convex polygons and the Birkhoff--Poritsky conjecture
Leonid Bunimovich, Roberta Shapiro
We prove that the billiard claimed to be a possible counterexample to the Birkhoff-Poritsky conjecture is actually not a counterexample. We also show that for a billiard in a table…
Large flats in large subgraphs of fine curve graphs
Ryan Dickmann, Roberta Shapiro
The fine curve graph of a surface is a graph whose vertices are essential simple closed curves and whose edges connect disjoint curves. Following a rich history of hyperbolicity of…
Hyperbolicity, topology, and combinatorics of fine curve graphs and variants
Roberta Shapiro
Given a surface, the fine -curve graph of the surface is a graph whose vertices are simple closed essential curves and whose edges connect curves that intersect in at most p…
Automorphisms of the fine 1-curve graph
Katherine Williams Booth, Daniel Minahan, Roberta Shapiro
The fine 1-curve graph of a surface is a graph whose vertices are simple closed curves on the surface and whose edges connect vertices that intersect in at most one point. We show…
Homotopy types of fine curve and fine arc complexes
Ryan Dickmann, Zachary Himes, Alexander Nolte +1
The fine curve complex of a surface is a simplicial complex whose vertices are essential simple closed curves and whose -simplices are collections of disjoint curves. We p…
Property in Coexeter groups
Sahana Balasubramanya, Georgia Burkhalter, Rachel Niebler +1
A group has Property if it does not admit a loxodromic element in any hyperbolic action. In other words, a group with this property is inaccessible for study from t…