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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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Volume optimization, normal surfaces and Thurston's equation on triangulated 3-manifolds
by
Feng Luo
Rutgers University

We establish a relationship among the normal surface theory, Thurston's algebraic gluing equation for hyperbolic metrics and volume optimization of generalized angle structures on triangulated 3-manifolds. The main result shows that a critical point of the volume on generalized angle structures either produces a solution to Thurston's gluing equation or a branched normal surfaces with at most two quadrilateral types.

Date received: May 22, 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-11.