@article{ca5462d1f4334bb7bd22bef67a53a3f5,
title = "The FKB invariant is the 3d index",
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 KaniaBartoszynska for cusped hyperbolic 3-manifolds. Conversely, we identify the tetrahedron index of Dimofte–Gaiotto–Gukov as a limit of quantum 6j-symbols.",
keywords = "3-manifolds, 3D-index, ideal tetrahedron, Ideal triangulations, normal surfaces, quantum 6j-symbols, spines, tetrahedron index, TQFT, Turaev–Viro invariants",
author = "Stavros Garoufalidis and {van der Veen}, Roland",
note = "Funding Information: The second author wishes to thank the International Mathematics Center at SUSTech University, Shenzhen for their hospitality. The authors wish to thank Banff for inviting them at the conference on Modular Forms and Quantum Knot Invariants in March 2018 where the results were conceived. Publisher Copyright: {\textcopyright} 2023 European Mathematical Society.",
year = "2022",
doi = "10.4171/qt/171",
language = "English",
volume = "13",
pages = "525--538",
journal = "Quantum Topology",
issn = "1663-487X",
publisher = "EMS Press",
number = "3",
}