34 citations · 104 across the 17 of their papers we have counts for
20 papers
A Combinatorial Characterization of Sol 3-Manifolds
Daryl Cooper, Leslie Mavrakis, Priyam Patel
We show that there is a universal compact branched 3-manifold such that a closed 3-manifold immerses into if and only if admits a Sol structure. Equivalently, a clo…
Combinatorial Characterizations and Branched Manifolds
Daryl Cooper, Leslie Mavrakis, Priyam Patel
A family of compact n-manifolds is locally combinatorially defined (LCD) if it can be specified by a finite number of local triangulations. We show that LCD is equivalent to the ex…
Shifts maps are not type-preserving
Carolyn Abbott, Nicholas Miller, Priyam Patel
For a surface of sufficient complexity, Dehn twists act elliptically on the arc, curve, and relative arc graph of . We show that composing a Dehn twist with a shift map resu…
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.
Thurston's Theorem: Entropy in Dimension One
Ryan Dickmann, George Domat, Thomas Hill +4
In his paper, Thurston shows that a positive real number is the topological entropy for an ergodic traintrack representative of an outer automorphism of a free group if and onl…
Infinite-type loxodromic isometries of the relative arc graph
Carolyn R. Abbott, Nicholas Miller, Priyam Patel
An infinite-type surface is of type if it has an isolated puncture and admits shift maps. This includes all infinite-type surfaces with an isolated puncture o…
A new construction of subgroups of big mapping class groups
Carolyn R. Abbott, Hannah Hoganson, Marissa Loving +2
We explicitly construct new subgroups of the mapping class groups of an uncountable collection of infinite-type surfaces, including, but not limited to, free groups, Baumslag-Solit…
Stable commutator length on big mapping class groups
Elizabeth Field, Priyam Patel, Alexander J. Rasmussen
We study stable commutator length on mapping class groups of certain infinite-type surfaces. In particular, we show that stable commutator length defines a continuous function on t…
Free products from spinning and rotating families
Mladen Bestvina, Ryan Dickmann, George Domat +3
The far-reaching work of Dahmani-Guirardel-Osin and recent work of Clay-Mangahas-Margalit provide geometric approaches to the study of the normal closure of a subgroup (or a collec…
Isometry groups of infinite-genus hyperbolic surfaces
Tarik Aougab, Priyam Patel, Nicholas G. Vlamis
Given a 2-manifold, a fundamental question to ask is which groups can be realized as the isometry group of a Riemannan metric of constant curvature on the manifold. In this paper,…
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…
Effective virtual and residual properties of some arithmetic hyperbolic 3-manifolds
Jason DeBlois, Nicholas Miller, Priyam Patel
We give an effective upper bound, for certain arithmetic hyperbolic 3-manifold groups obtained from a quadratic form construction, on the minimal index of a subgroup that embeds in…
The first integral cohomology of pure mapping class groups
Javier Aramayona, Priyam Patel, Nicholas G. Vlamis
It is a classical result of Powell that pure mapping class groups of connected, orientable surfaces of finite type and genus at least three are perfect. In stark contrast, we const…
Algebraic and topological properties of big mapping class groups
Priyam Patel, Nicholas G. Vlamis
Let be an orientable, connected surface with infinitely-generated fundamental group. The main theorem states that if the genus of is finite and at least 4, then the isomorp…
Building hyperbolic metrics suited to closed curves and applications to lifting simply
Tarik Aougab, Jonah Gaster, Priyam Patel +1
Let be an essential closed curve with at most self-intersections on a surface with negative Euler characteristic. In this paper, we construct a hyperbolic met…
Zariski Closures and Subgroup Separability
Larsen Louder, D. B. McReynolds, Priyam Patel
The main result of this article is a refinement of the well-known subgroup separability results of Hall and Scott for free and surface groups. We show that for any finitely generat…
Quantifying separability in virtually special groups
Mark F. Hagen, Priyam Patel
We give a new, effective proof of the separability of cubically convex-cocompact subgroups of special groups. As a consequence, we show that if is a virtually compact special h…
On the Residual Finiteness Growths of Particular Hyperbolic Manifold Groups
Priyam Patel
We give a quantification of residual finiteness for the fundamental groups of hyperbolic manifolds that admit a totally geodesic immersion to a compact, right-angled Coxeter orbifo…
Residual Finiteness Growths of Virtually Special Groups
Khalid Bou-Rabee, Mark F. Hagen, Priyam Patel
Let be a virtually special group. Then the residual finiteness growth of is at most linear. This result cannot be found by embedding into a special linear group. Indeed…
On a Theorem of Peter Scott
Priyam Patel
We quantify Peter Scott's Theorem that surface groups are locally extended residually finite (LERF) in terms of geometric data. In the process, we will quantify another result by S…