Volume 17, issue 2 (2017)

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Infima of length functions and dual cube complexes

Jonah Gaster

Algebraic & Geometric Topology 17 (2017) 1041–1057
Abstract

In the presence of certain topological conditions, we provide lower bounds for the infimum of the length function associated to a collection of curves on Teichmüller space that depend on the dual cube complex associated to the collection, a concept due to Sageev. As an application of our bounds, we obtain estimates for the “longest” curve with $k$ self-intersections, complementing work of Basmajian [J. Topol. 6 (2013) 513–524].

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Keywords
closed curves on surfaces, hyperbolic surfaces, CAT(0) cube complexes, surface groups
Primary: 51M10
Secondary: 51M16