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A second time around the Volume Conjecture
May 30 - June 3, 2007
Louisiana State University
Baton Rouge, LA, USA

Organizers
Abhijit Champanerkar, Oliver Dasbach, Effie Kalfagianni, Ilya Kofman, Walter Neumann, Neal Stoltzfus

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The cosine law, volume and the Teichmüller space
by
Feng Luo
Rutgers University

We discuss some relationships between the cosine law, volume in dimension-3 and the Teichmüller space.

The cosine law for triangles in the sphere, the plane or the hyperbolic plane takes different forms. However, derivatives of these cosine laws satisfy the same identities. We will show that the Schlaefli formula for 3-dimensional volume can be derived from these identities. Furthermore, in dimension-3, this seems to suggests a way to "complexify" the volume. As another application of these identities, we produce a time dependent family of coordinates for the Teichmüller space of a surface with boundary.

Date received: May 1, 2007

Copyright © 2007 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 # caus-03.