2012/08/08 by Stavros Garoufalidis, Garoufalidis, Stavros · 2 citations
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT
paper · pdf · doi:10.48550/arxiv.1208.1663
28 pages, 11 figures
arxiv created 2015/10/07 · arxiv updated 2015/10/08
The 3D index of Dimofte-Gaiotto-Gukov a partially defined function on the set of ideal triangulations of 3-manifolds with r torii boundary components. For a fixed 2r tuple of integers, the index takes values in the set of q-series with integer coefficients. Our goal is to give an axiomatic definition of the tetrahedron index, and a proof that the domain of the 3D index consists precisely of the set of ideal triangulations that support an index structure. The latter is a generalization of a strict angle structure. We also prove that the 3D index is invariant under 3-2 moves, but not in general under 2-3 moves.