Homological Algebra of Knots and BPS States

  title={Homological Algebra of Knots and BPS States},
  author={Sergei Gukov and Marko Sto{\vs}i{\'c}},
It is known that knot homologies admit a physical description as spaces of open BPS states. We study operators and algebras acting on these spaces. This leads to a very rich story, which involves wall crossing phenomena, algebras of closed BPS states acting on spaces of open BPS states, and deformations of Landau-Ginzburg models. One important application to knot homologies is the existence of "colored differentials" that relate homological invariants of knots colored by different… CONTINUE READING


Publications citing this paper.