### University of Arkansas Topology Seminar: 11/1/2013

### Speaker: Henry Segerman

### Title: Regular triangulations and the index of a cusped hyperbolic
3-manifold

Abstract: 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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