Triangulation independent Ptolemy varieties

Series
Geometry Topology Seminar
Time
Monday, October 26, 2015 - 2:05pm for 1 hour (actually 50 minutes)
Location
Skiles 270
Speaker
Christian Zickert – University of Maryland – zickert@math.umd.eduhttp://www.math.umd.edu/~zickert/
Organizer
Stavros Garoufalidis
The Ptolemy variety is an invariant of a triangulated 3-manifoldM. It detects SL(2,C)-representations of pi_1(M) in the sense that everypoint in the Ptolemy variety canonically determines a representation (up toconjugation). It is closely related to Thurston's gluing equation varietyfor PSL(2,C)-representations. Unfortunately, both the gluing equationvariety and the Ptolemy variety depend on the triangulation and may missseveral components of representations. We discuss the basic properties ofthese varieties, how to compute invariants such as trace fields and complexvolume, and how to obtain a variety, which is independent of thetriangulation.