3d-3d correspondence and abelian flat connection

A bstract We realize a homological block of a knot complement in S 3 for G ℂ = SL(2, ℂ ) as a half-index of a 3d $$ \mathcal{N} $$ N = 2 theory via an expression of the homological block as an inverted Habiro series by working out some examples, which we expect to extend to general knots. Also, by choosing a certain set of poles in the integral expression of the half-index, we obtain the colored Jones polynomial.