Basmajian's identity in higher Teichmüller-Thurston theory

Nicholas G. Vlamis, Andrew Yarmola

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We prove an extension of Basmajian's identity to n-Hitchin representations of compact bordered surfaces. For n = 3, we show that this identity has a geometric interpretation for convex real projective structures analogous to Basmajian's original result. As part of our proof, we demonstrate that, with respect to the Lebesgue measure on the Frenet curve associated to a Hitchin representation, the limit set of an incompressible subsurface of a closed surface has measure zero. This generalizes a classical result in hyperbolic geometry. Finally, we recall the Labourie-McShane extension of the McShane-Mirzakhani identity to Hitchin representations and note a close connection to Basmajian's identity in both the hyperbolic and the Hitchin settings.

Original languageEnglish (US)
Pages (from-to)744-764
Number of pages21
JournalJournal of Topology
Volume10
Issue number3
DOIs
StatePublished - Jan 1 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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