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Topology/Geometry Seminar

A relative version of the Turaev-Viro invariants and hyperbolic polyhedral metrics

Tian Yang (TAMU)

Location:  zoom link:
Date & time: Tuesday, 29 September 2020 at 3:50PM - 4:50PM

We define a relative version of the Turaev-Viro invariants for an ideally triangulated compact 3-manifold with non-empty boundary and a coloring on the edges, and propose the Volume Conjecture for these invariants whose asymptotic behavior is related to the volume of the manifold in the hyperbolic polyhedral metric with singular locus the edges and cone angles determined by the coloring. As the main result of this talk, we prove the conjecture in the case that the cone angles are sufficiently small. This suggests an approach of solving the Volume Conjecture for the Turaev-Viro invariants of hyperbolic 3-manifold with totally geodesic boundary.

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