8 papers
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 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…
Quasi-isometric rigidity of the integers: an elementary primer
Tarik Aougab, Hikaru Jitsukawa, Kim Ruane
Chatawate (Flame) Ruethaimetapat was a passionate, enthusiastic, and wonderful person who passed away in August of 2024. At the time of their passing they were working towards thei…
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…
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…
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…