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I will give an overview of a "3d-3d" relation that assigns 3d supersymmetric gauge theories (T[M]) to topological 3-manifolds (M). Physically, the gauge theories come from wrapping M5 branes on M.
They can be assembled explicitly and axiomatically using an ideal tetrahedral decomposition of M, together with TQFT-like gluing rules.
Various geometric invariants of M (such as SL(N,C) Chern-Simons partition functions) match field-theoretic observables (such as partition functions and indices) of T[M].