arXiv subjects

Sarah C. Mousley

Publications and source records attributed to Sarah C. Mousley.

3 recordsLinked to original sources

arXiv2018

Hierarchically hyperbolic groups are determined by their Morse boundaries

We generalize a result of Paulin on the Gromov boundary of hyperbolic groups to the Morse boundary of proper, maximal hierarchically hyperbolic spaces admitting cocompact group actions by isometries. Namely we show that if the Morse boundaries of two such spaces each contain at least three points, then the spaces are quasi-isometric if and only if there exists a 2-stable, quasi-möbius homeomorphism between their Morse boundaries. Our result extends a recent result of Charney-Murray, who prove such a classification for CAT(0) groups, and is new for mapping class groups and the fundamental groups of $3$-manifolds without Nil or Sol components.

math.GT↗

arXiv2017

Exotic limit sets of Teichmüller geodesics in the HHS boundary

We answer a question of Durham, Hagen, and Sisto, proving that a Teichmüller geodesic ray does not necessarily converge to a unique point in the hierarchically hyperbolic space boundary of Teichmüller space. In fact, we prove that the limit set can be almost anything allowed by the topology.

math.GT↗

arXiv2016

Non-existence of boundary maps for some hierarchically hyperbolic spaces

We provide negative answers to questions posed by Durham, Hagen, and Sisto on the existence of boundary maps for some hierarchically hyperbolic spaces, namely maps from right-angled Artin groups to mapping class groups. We also prove results on existence of boundary maps for free subgroups of mapping class groups.

math.GT↗