On the geometry of graphs associated to infinite-type surfaces
Abstract
Consider a connected orientable surface S of infinite topological type, i.e. with infinitely-generated fundamental group. We describe the large-scale geometry of arbitrary connected subgraphs of the arc complex A(S) and curve complex C(S) of S, provided they are invariant under a sufficiently big subgroup of the mapping class group Mod(S). We obtain a number of consequences; in particular we recover the main results of J. Bavard and Aramayona-Fossas-Parlier .
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