New York Journal of Mathematics
Volume 24 (2018) 167-181


Arpan Kabiraj

Equal angles of intersecting geodesics for every hyperbolic metric

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Published: January 30, 2018
Keywords: Goldman bracket, geometric intersection number, Teichm├╝ller space
Subject: 57M50 57M07


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.


The author is supported by the Department of Science & Technology (DST); INSPIRE faculty.

Author information

Department of Mathematics, Chennai Mathematical Institute, Chennai 603103, India