3 papers
math.GT2026
Gromov boundary of the Grand Arc graph
Carolyn Abbott, Assaf Bar-Natan, Arya Vadnere
We describe a dense subset of the Gromov boundary of the grand arc graph of an infinite-type surface as a space of geodesic laminations, analogous to Klarreich's description of the…
math.GT2026
The non-peripheral curve graph and divergence in big mapping class groups
Assaf Bar-Natan, Yulan Qing, Kasra Rafi
We introduce a numerical invariant measuring the end-complexity of and use it to organize coarse-geometric features of Map(). Our main tool is the \emph{non-perip…
math.GT2025
Convex structures of the unit tangent spheres in Teichm{ü}ller space
Assaf Bar-Natan, Ken'Ichi Ohshika, Athanase Papadopoulos
We analyse the convex structure of the Finsler infinitesimal balls of the Thurston metric on Teichm{ü}ller space. We analyse the convex structure of the Finsler unit ball in the t…