Fivebranes and 3-manifold homology

Fivebranes and 3-manifold homology

Blog Article

Abstract Motivated by physical constructions of homological knot invariants, the gel bottle audrey we study their analogs for closed 3-manifolds.We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds.In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N = 2 $$ mathcal{N}=2 $$ theory T[M 3] on a Riemann surface with defects.We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology.The latter gives a categorification of Chern-Simons partition function.

Some of the new key elements include the explicit form of the S-transform and a novel connection between red pygmy dogwood categorification and a previously mysterious role of Eichler integrals in Chern-Simons theory.