9 citations · 24 across the 13 of their papers we have counts for
13 papers
The complex of cuts in a Stone space
Beth Branman, Robert Alonzo Lyman
Stone's representation theorem asserts a duality between Boolean algebras on the one hand and Stone space, which are compact, Hausdorff, and totally disconnected, on the other. Thi…
Low complexity among principal fully irreducible elements of Out()
Naomi Andrew, Paige Hillen, Robert Alonzo Lyman +1
We find the shortest realized stretch factor for a fully irreducible and show that it is realized by a "principal" fully irreducible element. We also show t…
One-endedness of outer automorphism groups of free products of finite and cyclic groups
Rylee Alanza Lyman
The main result of this paper is that the outer automorphism group of a free product of finite groups and cyclic groups is semistable at infinity (provided it is one ended) or semi…
When is the Outer Space of a free product CAT(0)?
Robert Alonzo Lyman
Generalizing Culler and Vogtmann's Outer Space for the free group, Guirardel and Levitt construct an Outer Space for a free product of groups. We completely characterize when this…
On Whitehead's cut vertex lemma
Rylee Alanza Lyman
One version of Whitehead's famous cut vertex lemma says that if an element of a free group is part of a free basis, then a certain graph associated to its conjugacy class that we c…
CTs for free products
Rylee Alanza Lyman
The fundamental group of a finite graph of groups with trivial edge groups is a free product. We are interested in those outer automorphisms of such a free product that permute the…
Lipschitz metric isometries between Outer Spaces of virtually free groups
Rylee Alanza Lyman
Dowdall and Taylor observed that given a finite-index subgroup of a free group, taking covers induces an embedding from the Outer Space of the free group to the Outer Space of the…
Train track maps on graphs of groups
Rylee Alanza Lyman
In this paper we develop the theory of train track maps on graphs of groups. Expanding a definition of Bass, we define a notion of a map of a graph of groups, and of a homotopy equ…
Extensions of hyperbolic groups have locally uniform exponential growth
Robert Kropholler, Rylee Alanza Lyman, Thomas Ng
We introduce a quantitative characterization of subgroup alternatives modeled on the Tits alternative in terms of group laws and investigate when this property is preserved under e…
Folding-like techniques for CAT(0) cube complexes
Michael Ben-Zvi, Robert Kropholler, Rylee Alanza Lyman
In a seminal paper, Stallings introduced folding of morphisms of graphs. One consequence of folding is the representation of finitely-generated subgroups of a finite-rank free grou…
Train Tracks on Graphs of Groups and Outer Automorphisms of Hyperbolic Groups
Rylee Alanza Lyman
Stallings remarked that an outer automorphism of a free group may be thought of as a subdivision of a graph followed by a sequence of folds. In this thesis, we prove that automorph…
Nielsen realization for infinite-type surfaces
Santana Afton, Danny Calegari, Lvzhou Chen +1
Given a finite subgroup G of the mapping class group of a surface S, the Nielsen realization problem asks whether G can be realized as a finite group of homeomorphisms of S. In 198…
Some new CAT(0) free-by-cyclic groups
Rylee Alanza Lyman
We show the existence of several new infinite families of polynomially-growing automorphisms of free groups whose mapping tori are CAT(0) free-by-cyclic groups. Such mapping tori a…