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Equal Angles of Intersecting Geodesics for Every Hyperbolic Metric by Kabiraj, Arpan is a scholarly article available to read on EtoBox.

What is Equal Angles of Intersecting Geodesics for Every Hyperbolic Metric about?

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.

Author

Kabiraj, Arpan

Published

2016

Language

EN