## 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 language | English |
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Pages (from-to) | 167-181 |

Number of pages | 15 |

Journal | New York Journal of Mathematics |

Volume | 24 |

State | Published - 30 Jan 2018 |

Externally published | Yes |

## Keywords

- Geometric intersection number
- Goldman bracket
- Teichmüller space

## ASJC Scopus subject areas

- General Mathematics