The FKB invariant is the 3d index

2020/02/29 by Garoufalidis, Stavros, van der Veen, Roland
#FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2003.00283

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.

Related

• The 3d-index of the 3d-skein module via the quantum trace map
• The descendants of the 3d-index
• Perturbative invariants of cusped hyperbolic 3-manifolds
• The 3D index and Dehn filling
• QHI Theory, II: Dilogarithmic and Quantum Hyperbolic Invariants of 3-Manifolds with PSL(2,C)-Characters