Infima of length functions and dual cube complexes
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 Teichm\"uller 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 basmajian.
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