The FKB invariant is the 3d index

Stavros Garoufalidis; Roland van der Veen

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arXiv · 2003.00283

The FKB invariant is the 3d index

Stavros Garoufalidis·Roland van der Veen

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Abstract

We identify the q-series associated to an 1-efficient ideal triangulation of a cusped hyperbolic 3-manifold by Frohman and Kania-Bartoszynska with the 3D-index of Dimofte-Gaiotto-Gukov. This implies the topological invariance of the $q$-series of Frohman and Kania-Bartoszynska for cusped hyperbolic 3-manifolds. Conversely, we identify the tetrahedron index of Dimofte-Gaiotto-Gukov as a limit of quantum 6j-symbols.

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Stavros Garoufalidis, Roland van der Veen. 2020-02-29. The FKB invariant is the 3d index. https://arxiv.org/abs/2003.00283

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