31 citations · 100 across the 28 of their papers we have counts for
7 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 a collection of simple closed curves pairwise intersecting at most once on an orientable surface of Euler characteristic has at most curves. Up…
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…
Constructing reducibly geometrically finite subgroups of the mapping class group
Tarik Aougab, Harrison Bray, Spencer Dowdall +3
In this article, we consider qualified notions of geometric finiteness in mapping class groups called parabolically geometrically finite (PGF) and reducibly geometrically finite (R…