34 citations · 60 across the 7 of their papers we have counts for
9 papers · 1 filter
Towards the boundary of the fine curve graph
Jonathan Bowden, Sebastian Hensel, Richard Webb
The fine curve graph was introduced as a geometric tool to study homeomorphisms of surfaces. In this paper we study the Gromov boundary of this space and the local topology near po…
Contractible, hyperbolic but non-CAT(0) complexes
Richard C. H. Webb
We prove that almost all arc complexes do not admit a CAT(0) metric with finitely many shapes, in particular any finite-index subgroup of the mapping class group does not preserve…
Quasi-morphisms on surface diffeomorphism groups
Jonathan Bowden, Sebastian Hensel, Richard Webb
We show that the identity component of the group of diffeomorphisms of a closed oriented surface of positive genus admits many unbounded quasi-morphisms. As a corollary, we also de…
Polynomial-time algorithms for the curve graph
Mark C. Bell, Richard C. H. Webb
We describe a polynomial-time algorithm to compute a (tight) geodesic between two curves in the curve graph. As well as enabling us to compute the distance between a pair of curves…
Applications of fast triangulation simplification
Mark C. Bell, Richard C. H. Webb
We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs…
Shadows of Teichmüller discs in the curve graph
Robert Tang, Richard C. H. Webb
We consider several natural sets of curves associated to a given Teichmüller disc, such as the systole set or cylinder set, and study their coarse geometry inside the curve graph.…