Equal angles of intersecting geodesics for every hyperbolic metric

Arpan Kabiraj

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We study the geometric properties of the terms of the Goldman bracket between two free homotopy classes of oriented closed curves in a hyperbolic surface. We provide an obstruction for the equality of two terms in the Goldman bracket, namely if two terms in the Goldman bracket are equal to each other then for every hyperbolic metric, the angles corresponding to the intersection points are equal to each other. As a consequence, we obtain an alternative proof of a theorem of Chas, i.e., if one of the free homotopy classes contains a simple representative then the geometric intersection number and the number of terms (counted with multiplicity) in the Goldman bracket are the same.

Original languageEnglish
Pages (from-to)167-181
Number of pages15
JournalNew York Journal of Mathematics
Volume24
StatePublished - 30 Jan 2018
Externally publishedYes

Keywords

  • Geometric intersection number
  • Goldman bracket
  • Teichmüller space

ASJC Scopus subject areas

  • Mathematics (all)

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