8 citations · 9 across the 8 of their papers we have counts for
11 papers
Largest hyperbolic actions of 3--manifold groups
Carolyn Abbott, Hoang Thanh Nguyen, Alexander J. Rasmussen
The set of equivalence classes of cobounded actions of a group G on different hyperbolic metric spaces carries a natural partial order. Following Abbott--Balasubramanya--Osin, the…
Transverse measures to infinite type laminations
Mladen Bestvina, Alexander J. Rasmussen
We study the cone of transverse measures to a fixed geodesic lamination on an infinite type hyperbolic surface. Under simple hypotheses on the metric, we give an explicit descripti…
Valuations, completions, and hyperbolic actions of metabelian groups
Carolyn R. Abbott, Sahana Balasubramanya, Sam Payne +1
Actions on hyperbolic metric spaces are an important tool for studying groups, and so it is natural, but difficult, to attempt to classify all such actions of a fixed group. In thi…
Higher rank confining subsets and hyperbolic actions of solvable groups
Carolyn R. Abbott, Sahana Balasubramanya, Alexander J. Rasmussen
Recent papers of the authors have completely described the hyperbolic actions of several families of classically studied solvable groups. A key tool for these investigations is the…
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…
Laminations and 2-filling rays on infinite type surfaces
Lvzhou Chen, Alexander J. Rasmussen
The loop graph of an infinite type surface is an infinite diameter hyperbolic graph first studied in detail by Juliette Bavard. An important open problem in the study of infinite t…
Largest hyperbolic actions and quasi-parabolic actions in groups
Carolyn R. Abbott, Alexander J. Rasmussen
The set of equivalence classes of cobounded actions of a group on different hyperbolic metric spaces carries a natural partial order. The resulting poset thus gives rise to a notio…
Geometry of the graphs of nonseparating curves: covers and boundaries
Alexander J. Rasmussen
We investigate the geometry of the graphs of nonseparating curves for surfaces of finite positive genus with potentially infinitely many punctures. This graph has infinite diameter…
WWPD elements of big mapping class groups
Alexander J. Rasmussen
We study mapping class groups of infinite type surfaces with isolated punctures and their actions on the loop graphs introduced by Bavard-Walker. We classify all of the mapping cla…
Actions of solvable Baumslag-Solitar groups on hyperbolic metric spaces
Carolyn R. Abbott, Alexander J. Rasmussen
We give a complete list of the cobounded actions of solvable Baumslag-Solitar groups on hyperbolic metric spaces up to a natural equivalence relation. The set of equivalence classe…
Uniform hyperbolicity of the graphs of nonseparating curves via bicorn curves
Alexander J. Rasmussen
We show that the graphs of nonseparating curves for oriented finite type surfaces are uniformly hyperbolic. Our proof follows the proof of uniform hyperbolicity of the graphs of cu…