10 citations · 30 across the 11 of their papers we have counts for
14 papers
The word problem for the mapping class group in quasi-linear time
Mark C. Bell, Saul Schleimer
We give an -time algorithm for the word problem in the mapping class group of a compact surface.
Diagonal flow detects topology of strata
Mark Bell, Vincent Delecroix, Vaibhav Gadre +2
We study the interplay between the diagonal flow on, and the topology of, a stratum component of a space of rooted quadratic differentials. We prove that the flow group -- the subg…
Experimental statistics for Mirzakhani's Theorem
Mark C Bell
In her seminal 2008 paper, Maryam Mirzakhani showed that the ratio that two topological types of curves occur in is a rational number. In this paper we describe the process by whic…
Coding Teichmüller flow using veering triangulations
Mark Bell, Vincent Delecroix, Vaibhav Gadre +2
We develop the theory of veering triangulations on oriented surfaces adapted to moduli spaces of half-translation surfaces. We use veering triangulations to give a coding of the Te…
Computing trisections of 4-manifolds
Mark Bell, Joel Hass, J. Hyam Rubinstein +1
Algorithms that decompose a manifold into simple pieces reveal the geometric and topological structure of the manifold, showing how complicated structures are constructed from simp…
Cubical Geometry in the Polygonalisation Complex
Mark C. Bell, Valentina Disarlo, Robert Tang
We introduce the polygonalisation complex of a surface, a cube complex whose vertices correspond to polygonalisations. This is a geometric model for the mapping class group and it…