61 citations · 219 across the 26 of their papers we have counts for
35 papers
Endperiodic maps via pseudo-Anosov flows
Michael P. Landry, Yair N. Minsky, Samuel J. Taylor
We show that every atoroidal endperiodic map of an infinite-type surface can be obtained from a depth one foliation in a fibered hyperbolic 3-manifold, reversing a well-known const…
Constructing endperiodic loxodromics of infinite-type arc graphs
Priyam Patel, Samuel J. Taylor
We give general conditions to produce endperiodic homeomorphisms that act loxodromically on various arc graphs of infinite-type surfaces.
Equidistribution of hyperbolic groups in homogeneous spaces
Ilya Gekhtman, Samuel J. Taylor, Giulio Tiozzo
We prove that infinite orbits of Zariski dense hyperbolic groups equidistribute in homogeneous spaces, in the sense that the family of measures obtained by averaging along spheres…
Orientable maps and polynomial invariants of free-by-cyclic groups
Spencer Dowdall, Radhika Gupta, Samuel J. Taylor
We relate the McMullen polynomial of a free-by-cyclic group to its Alexander polynomial. To do so, we introduce the notion of an orientable fully irreducible outer automorphism …
Subsurface distances for hyperbolic 3-manifolds fibering over the circle
Yair N. Minsky, Samuel J. Taylor
For a hyperbolic fibered 3-manifold M, we prove results that uniformly relate the structure of surface projections as one varies the fibrations of M. This extends our previous work…
Flows, growth rates, and the veering polynomial
Michael P. Landry, Yair N. Minsky, Samuel J. Taylor
For certain pseudo-Anosov flows on closed -manifolds, unpublished work of Agol--Guéritaud produces a veering triangulation on the manifold obtained by deleting 's…
A polynomial invariant for veering triangulations
Michael Landry, Yair N. Minsky, Samuel J. Taylor
We introduce a polynomial invariant associated to a veering triangulation of a -manifold . In the special case where the triang…
Central limit theorems for counting measures in coarse negative curvature
Ilya Gekhtman, Samuel J. Taylor, Giulio Tiozzo
We establish central limit theorems for an action of a group G on a hyperbolic space X with respect to the counting measure on a Cayley graph of G. Our techniques allow us to remov…
Weil-Petersson translation length and manifolds with many fibered fillings
Christopher J. Leininger, Yair N. Minsky, Juan Souto +1
We prove that any mapping torus of a pseudo-Anosov mapping class with bounded normalized Weil-Petersson translation length contains a finite set of transverse and level closed curv…
Random trees in the boundary of Outer space
Ilya Kapovich, Joseph Maher, Catherine Pfaff +1
We prove that for the harmonic measure associated to a random walk on Out satisfying some mild conditions, a typical tree in the boundary of Outer space is trivalent and non…
Covers of surfaces, Kleinian groups, and the curve complex
Tarik Aougab, Priyam Patel, Samuel J. Taylor
We prove an effective version of a theorem relating curve complex distance to electric distance in hyperbolic 3-manifolds, up to errors that are polynomial in the complexity of the…
A central limit theorem for random closed geodesics: proof of the Chas-Li-Maskit conjecture
Ilya Gekhtman, Samuel J. Taylor, Giulio Tiozzo
We prove a central limit theorem for the length of closed geodesics in any compact orientable hyperbolic surface. In the special case of a hyperbolic pair of pants, this settles a…
Random veering triangulations are not geometric
David Futer, Samuel J. Taylor, William Worden
Every pseudo-Anosov mapping class defines an associated veering triangulation of a punctured mapping torus. We show that generically, is not geometric. Here, the wo…
Random outer automorphisms of free groups: Attracting trees and their singularity structures
Ilya Kapovich, Joseph Maher, Catherine Pfaff +1
We prove that a "random" free group outer automorphism is an ageometric fully irreducible outer automorphism whose ideal Whitehead graph is a union of triangles. In particular, we…
Counting problems in graph products and relatively hyperbolic groups
Ilya Gekhtman, Samuel J. Taylor, Giulio Tiozzo
We study properties of generic elements of groups of isometries of hyperbolic spaces. Under general combinatorial conditions, we prove that loxodromic elements are generic (i.e. th…
Rank and Nielsen equivalence in hyperbolic extensions
Spencer Dowdall, Samuel J. Taylor
In this note, we generalize a theorem of Juan Souto on rank and Nielsen equivalence in the fundamental group of a hyperbolic fibered 3-manifold to a large class of hyperbolic group…
Intersection properties of stable subgroups and bounded cohomology
Yago Antolín, Mahan Mj, Alessandro Sisto +1
We show that a finite collection of stable subgroups of a finitely generated group has finite height, finite width and bounded packing. We then use knowledge about intersections of…
Largest projections for random walks and shortest curves in random mapping tori
Alessandro Sisto, Samuel J. Taylor
We show that the largest subsurface projection distance between a marking and its image under the nth step of a random walk grows logarithmically in n, with probability approaching…
Pulling back stability with applications to Out() and relatively hyperbolic groups
Tarik Aougab, Matthew Gentry Durham, Samuel J. Taylor
We prove that stability -- a strong quasiconvexity property -- pulls back under proper actions on proper metric spaces. This result has several applications, including that convex…
Counting loxodromics for hyperbolic actions
Ilya Gekhtman, Samuel J. Taylor, Giulio Tiozzo
Let be a nonelementary action by isometries of a hyperbolic group on a hyperbolic metric space . We show that the set of elements of which act as…
Fibered faces, veering triangulations, and the arc complex
Yair N. Minsky, Samuel J. Taylor
We study the connections between subsurface projections in curve and arc complexes in fibered 3-manifolds and Agol's veering triangulation. The main theme is that large-distance su…
The co-surface graph and the geometry of hyperbolic free group extensions
Spencer Dowdall, Samuel J. Taylor
We introduce the co-surface graph of a finitely generated free group and use it to study the geometry of hyperbolic group extensions of . Am…
Pseudo-Anosovs optimizing the ratio of Teichmüller to curve graph translation length
Tarik Aougab, Samuel J. Taylor
Given a pseudo-Anosov map, let denote the translation length of in the Teichmüller space, and let denote the stable translation…
Cannon-Thurston maps for hyperbolic free group extensions
Spencer Dowdall, Ilya Kapovich, Samuel J. Taylor
This paper gives a detailed analysis of the Cannon--Thurston maps associated to a general class of hyperbolic free group extensions. Let denote a free groups of finite rank $…