5 papers · 1 filter
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…
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.
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…
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…