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Asymptotic dimension of graphs of arcs and curves on infinite-type surfaces

Michael Kopreski ⟨michaelkopreski@gmail.com⟩

Abstract:

In analogy to the curve complex and its role in the geometry of mapping class groups of finite-type surfaces, a number of authors have defined graphs whose vertices are arcs or curves on a given infinite-type surface S, and on which the mapping class group Map(S) acts by isometries. We show that for a broad class of such graphs, including the grand arc graph, the omnipresent arc graph, and all others defined comparably to Masur-Minsky, the asymptotic dimension is infinite. In particular, if one could construct a graph in this class admitting a Švarc-Milnor-type action of Map(S), then Map(S) would have infinite asymptotic dimension.

Scheduled for: 2025-03-08 10:45 AM: Michael Kopreski in Forbes 2070E

Status: Accepted

Collection: Geometric Group Theory

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