Infima of length functions and dual cube complexes

Gaster, Jonah

doi:10.2140/agt.2017.17.1041

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Infima of length functions and dual cube complexes

Jonah Gaster

Algebraic & Geometric Topology 17 (2017) 1041–1057

DOI: 10.2140/agt.2017.17.1041

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].

Keywords

closed curves on surfaces, hyperbolic surfaces, CAT(0) cube complexes, surface groups

Mathematical Subject Classification 2010

Primary: 51M10

Secondary: 51M16

References

Publication

Received: 11 January 2016

Revised: 21 June 2016

Accepted: 11 July 2016

Published: 14 March 2017

Authors

Jonah Gaster
Department of Mathematics Boston College 140 Commonwealth Avenue Chestnut Hill, MA 02467 United States
http://www2.bc.edu/jonah-gaster

Volume 17, issue 2 (2017)