Shadows of Teichmüller discs in the curve graph

Robert Tang, Richard Webb

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Abstract

We consider several natural sets of curves associated to a given Teichmüller disc, such as the systole set or cylinder set, and study their coarse geometry inside the curve graph. We prove that these sets are quasiconvex and agree up to uniformly bounded Hausdorff distance. We describe two operations on curves and show that they approximate nearest point projections to their respective targets. Our techniques can be used to prove a bounded geodesic image theorem for a natural map from the curve graph to the filling multi-arc graph associated to a Teichmüller disc.
Original languageEnglish
Pages (from-to)3301–3341
JournalInternational Mathematics Research Notices
Volume2018
Issue number11
Early online date4 Feb 2017
DOIs
Publication statusPublished - Jun 2018

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