44 citations · 112 across the 13 of their papers we have counts for
21 papers
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…
Depth of free-by-cyclic groups
Spencer Dowdall, Yassine Guerch, Radhika Gupta +2
For a free group automorphism, we prove that its poset of attracting lamination orbits is a canonical invariant of the associated mapping torus. That is, if a free-by-cyclic group…
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…
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 …
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 $…
Discretely shrinking targets in moduli space
Spencer Dowdall, Grace Work
We consider the discrete shrinking target problem for Teichmüller geodesic flow on the moduli space of abelian or quadratic differentials and prove that the discrete geodesic traje…
Isomorphisms between big mapping class groups
Juliette Bavard, Spencer Dowdall, Kasra Rafi
We show that any isomorphism between mapping class groups of orientable infinite-type surfaces is induced by a homeomorphism between the surfaces. Our argument additionally applies…
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…
Endomorphisms, train track maps, and fully irreducible monodromies
Spencer Dowdall, Ilya Kapovich, Christopher J. Leininger
Any endomorphism of a finitely generated free group naturally descends to an injective endomorphism of its stable quotient. In this paper, we prove a geometric incarnation of this…
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 $…
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…
Unbounded asymmetry of stretch factors
Spencer Dowdall, Ilya Kapovich, Christopher J Leininger
A result of Handel-Mosher guarantees that the ratio of logarithms of stretch factors of any fully irreducible automorphism of the free group and its inverse is bounded by a c…
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…