Thurston's gluing equations for PGL(n,C)

Series: 
Geometry Topology Seminar
Tuesday, March 19, 2013 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
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University of Maryland
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 Thurston's gluing equations are polynomial equations invented byThurston to explicitly compute hyperbolic structures or, more generally, representations in PGL(2,C). This is done via so called shape coordinates.We generalize the shape coordinates to obtain a parametrization ofrepresentations in PGL(n,C). We give applications to quantum topology, anddiscuss an intriguing duality between the shape coordinates and thePtolemy coordinates of Garoufalidis-Thurston-Zickert. The shapecoordinates and Ptolemy coordinates can be viewed as 3-dimensional analogues of the X- and A-coordinates on higher Teichmuller spaces due toFock and Goncharov.