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Infima of length functions and dual cube complexes. (English) Zbl 1379.30032
Author’s 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 A. Basmajian [J. Topol. 6, No. 2, 513–524 (2013; Zbl 1285.30024)].

##### MSC:
 30F60 Teichmüller theory for Riemann surfaces
##### Keywords:
closed curves on surfaces; Teichmüller space
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