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## Counting Closed Geodesics in Homology Classes for Convex Co-Compact Hyperbolic Manifolds.

### Jeffrey McGowan

Central Connecticut State University

###
Thursday, April 24, 2003

102 Bradley Hall, 4 pm

Tea 3:30 pm, Math Lounge

**Abstract: **
We consider manifolds $X= \Gamma\backslash \mathbb{H}^{n+1}$, where $\mathbb{H}^{n+1}$ is real hyperbolic $n+1$ space, and $\Gamma$ is a convex co-compact, discrete, torsion free group of isometries of $\mathbb{H}^{n+1}$. Using Selberg's trace formula (twisted by a character of the fundamental group of $X$), we compute the asymptotics of the counting function for closed geodesics in homology classes. For compact Riemann surfaces, this problem was studied by Katsada and Sunada, and Phillips and Sarnak. This is joint work with Peter Perry.

This talk will be accessible to graduate students.