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Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory
June 3-19, 2009
Columbia University
New York, USA

Organizers
Abhijit Champanerkar (CSI, CUNY), Oliver Dasbach (LSU), Effie Kalfagianni (MSU), Ilya Kofman (CSI, CUNY), Walter Neumann (Barnard College, Columbia U.), Neal Stoltzfus (LSU)

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How much rigid are the quantum hyperbolic invariants ?
by
Stephane Baseilhac
Institut Fourier, Universite de Grenoble

Quantum hyperbolic invariants can be defined for any compact oriented 3-manifold endowed with a holonomy representation in PSL(2,C). In the case of cusped hyperbolic manifolds, where the interior admits a complete finite volume hyperbolic metric with faithful and discrete holonomy, there is a natural "volume conjecture" relating the asymptotical growth rate of quantum hyperbolic invariants with the volume of the manifold. We will discuss this conjecture and some related problems, showing a crucial role of ideal points of the character variety.

Date received: June 13, 2009

Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cayy-39.