GTA Seminar: Segerman -- Regular Triangulations and the Index of a Cusped Hyperbolic 3-Manifold

Speaker: Henry Segerman (Melbourne)

http://www.ms.unimelb.edu.au/~segerman/

Time: Tuesday, Jan. 15, 12NOON--1PM

Room: Carslaw 707A

Lunch: after the talk. The reservation at Law Annex Cafe is 1:15PM. 

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Title: Regular Triangulations and the Index of a Cusped Hyperbolic 3-Manifold

Abstract: I will talk about recent work with Stavros Garoufalidis,
Craig Hodgson and Hyam Rubinstein. Recent work by Dimofte, Gaiotto and
Gukov defines the "index" (a collection of Laurent series) associated
to an ideal triangulation of an oriented cusped hyperbolic 3-manifold.
"Physics tells us" that this index should be a topological invariant
of the manifold, not just of the triangulation of it. The problem is
that the index is not well defined on all triangulations. We define a
class of triangulations of a 3-manifold, depending only on the
topology of the manifold, such that the index is well-defined and has
the same value for each triangulation in the class. A key requirement
is that the class of triangulations be connected by local moves on the
triangulations, since we can prove invariance of the index under these
moves. To achieve this requirement we import a result from the theory
of regular triangulations of Euclidean point configurations due to
Gelfand, Kapranov and Zelevinsky.

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Seminar website:

http://www.maths.usyd.edu.au/u/SemConf/Geometry/