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The FKB invariant is the 3d index
Published 29 Feb 2020 in math.GT and hep-th | (2003.00283v1)
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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