arXiv subjects
Publications and source records attributed to Marissa Chesser.
In this paper, we prove that for subgroups acting on admissible multiarc and curve graphs and for the handlebody group acting on the disk graph, the loxodromic elements are exactly those for which some pure power is a pseudo-Anosov on a witness. This generalizes the result of Masur and Minsky that the elements of the mapping class group that act loxodromically on the curve graph are the pseudo-Anosov elements.
We extend the characterization of stable subgroups of right-angled Artin groups of Koberda, Mangahas and Taylor to the case of graph products of infinite groups. Specifically, we show that the stable subgroups of such graph products are exactly the subgroups that quasi-isometrically embed in the associated contact graph. Equivalently, they are the subgroups that satisfy a condition arising from the defining graph: a stable subgroup is an almost join-free subgroup. In particular, we generalize the equivalence between stable and purely loxodromic subgroups from Koberda, Mangahas and Taylor in the case where all torsion subgroups of the vertex groups are finite, and the equivalence between stable and infinite index Morse subgroups from Tran in the case where the defining graph is connected.
In this paper, we introduce a graph coloring game called the Edge-Distinguishing Game (EDGe). The edge-distinguishing chromatic number of a graph is used to determine the moves each player can make. We determine which player has a winning strategy for particular graphs and graph families. Additionally, utilizing principles from game theory as well as previous work on a computational solution for the Game of Cycles.
In this note, we consider the notion of what we call recognizing spaces for stable subgroups of a given group. When a group $G$ is a mapping class group or right-angled Artin group, it is known that a subgroup is stable exactly when the largest acylindrical action $G \curvearrowright X$ provides a quasi-isometric embedding of the subgroup into $X$ via the orbit map. In this sense the largest acylindrical action for mapping class groups and right-angled Artin groups provides a recognizing space for all stable subgroups. In contrast, we construct an acylindrically hyperbolic group (relatively hyperbolic, in fact) whose largest acylindrical action does not recognize all stable subgroups.
We prove that finitely generated, purely pseudo-Anosov subgroups of the genus $2$ handlebody group are convex cocompact.
We show that a finitely generated subgroup of the genus two handlebody group is stable if and only if the orbit map to the disk graph is a quasi-isometric embedding. To this end, we prove that the genus two handlebody group is a hierarchically hyperbolic group, and that the maximal hyperbolic space in the hierarchy is quasi-isometric to the disk graph of a genus two handlebody by appealing to a construction of Hamenst\"adt-Hensel. We then utilize the characterization of stable subgroups of hierarchically hyperbolic groups provided by Abbott-Behrstock-Berlyne-Durham-Russell. We also present several applications of the main theorems, and show that the higher genus analogues of the genus two results do not hold.