9 citations · 10 across the 11 of their papers we have counts for
18 papers · 1 filter
Pseudo-Anosovs from the perspective of their mapping tori
Tarik Aougab
In this chapter, we outline some of the many combinatorial tools developed over the past three decades for studying a pseudo-Anosov diffeomorphism of a surface by analyzing the geo…
On fixed points of pseudo-Anosov maps
Tarik Aougab, David Futer, Samuel J. Taylor
We give a formula to estimate the number of fixed points of a pseudo-Anosov homeomorphism of a surface. When the homeomorphism satisfies a mild property called strong irreducibilit…
The arc complex is not quasi-isometric to the sphere complex
Tarik Aougab, Marissa Loving
We show that the arc complex is not quasi-isometric to the sphere complex associated to the double of a genus handlebody. Along the wa…
From arcs to curves: quadratic growth of 1-systems
Tarik Aougab, Jonah Gaster
We show that the largest size of a collection of simple closed curves pairwise intersecting at most once on an orientable surface of Euler characteristic grows quadratically in…
Subgraph Entropy
Tarik Aougab, Matt Clay, Tawfiq Hamed
Given , we prove that there exists depending only on so that if is a metric graph of rank with metric entropy , then there exists a proper subgraph $…
On the monodromy and spin parity of single-cylinder origamis in the minimal stratum
Tarik Aougab, Adam Friedman-Brown, Luke Jeffreys +1
In a paper with Menasco-Nieland, the first author constructed factorially many origamis in the minimal stratum of the moduli space of translation surfaces having simultaneously a s…