Fivebranes and 3-manifold homology

  title={Fivebranes and 3-manifold homology},
  author={Sergei Gukov and Pavel Putrov and Cumrun Vafa},
  journal={Journal of High Energy Physics},
A bstractMotivated by physical constructions of homological knot invariants, 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[M3] on a Riemann surface with defects. We demonstrate this by… 
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