44 citations · 112 across the 13 of their papers we have counts for
14 papers · 1 filter
Hierarchically Hyperbolic Surface-by-surface Groups
Spencer Dowdall, Matthew Gentry Durham, Chris Leininger +2
We give many examples of surface bundles over surfaces whose fundamental groups are hierarchically hyperbolic by showing that extensions of surface groups constructed by the third…
Counting mapping classes by Nielsen-Thurston type
Spencer Dowdall, Howard Masur
This paper concerns the lattice counting problem for the mapping class group of a surface acting on Teichmüller space with the Teichmüller metric. In that problem the goal is t…
Extensions of Veech groups II: Hierarchical hyperbolicity and quasi-isometric rigidity
Spencer Dowdall, Matthew G. Durham, Christopher J. Leininger +1
We show that for any lattice Veech group in the mapping class group of a closed surface , the associated --extension group is a hierarchically hyperboli…
Extensions of Veech groups I: A hyperbolic action
Spencer Dowdall, Matthew G. Durham, Christopher J. Leininger +1
Given a lattice Veech group in the mapping class group of a closed surface , this paper investigates the geometry of , the associated --extension group. We prove that $…
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…
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…
Contracting orbits in Outer space
Spencer Dowdall, Samuel J. Taylor
We show that strongly contracting geodesics in Outer space project to parameterized quasigeodesics in the free factor complex. This result provides a converse to a theorem of Bestv…
Hyperbolic extensions of free groups
Spencer Dowdall, Samuel J. Taylor
Given a finitely generated subgroup of the outer automorphism group of the rank free group , there is a corresponding free gro…
McMullen polynomials and Lipschitz flows for free-by-cyclic groups
Spencer Dowdall, Ilya Kapovich, Christopher J. Leininger
Consider a group G and an epimorphism u_0:G\to\Z inducing a splitting of G as a semidirect product ker(u_0)\rtimes_φ\Z with ker(u_0) a finitely generated free group and φ\in Out(ke…
Dynamics on free-by-cyclic groups
Spencer Dowdall, Ilya Kapovich, Christopher J. Leininger
Given a free-by-cyclic group determined by any outer automorphism which is represented by an expanding irreducible train-trac…
Pseudo-Anosov subgroups of fibered 3-manifold groups
Spencer Dowdall, Richard P. Kent, Christopher J. Leininger
Let X be a hyperbolic surface and H the fundamental group of a hyperbolic 3-manifold that fibers over the circle with fiber X. Using the Birman exact sequence, H embeds in the mapp…
Spheres in the curve complex
Spencer Dowdall, Moon Duchin, Howard Masur
In this paper we study the geometry of metric spheres in the curve complex of a surface, with the goal of determining the "average" distance between points on a given sphere. Avera…
Statistical hyperbolicity in Teichmüller space
Spencer Dowdall, Moon Duchin, Howard Masur
In this paper we explore the idea that Teichmüller space is hyperbolic "on average." Our approach focuses on studying the geometry of geodesics which spend a definite proportion of…
Dilatation versus self-intersection number for point-pushing pseudo-Anosov homeomorphisms
Spencer Dowdall
A filling curve on a based surface determines a pseudo-Anosov homeomorphism of via the process of "point-pushing along ." We consider the relationship between…