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arXiv · 1505.07944

Infima of length functions and dual cube complexes

Jonah Gaster
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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 \cite{basmajian}.

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Jonah Gaster. 2015-05-29. Infima of length functions and dual cube complexes. https://doi.org/10.2140/agt.2017.17.1041

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