TITLE: What else is Seiberg-Witten Theory equal to?
QUESTION [38 upvotes]: In low-dimensional topology there have been a bunch of invariants defined, and Seiberg-Witten Theory seems to make its appearance in [a lot of] them:
1) Heegaard Floer homology = SW Floer homology (Kutluhan, Lee, Taubes)
2) Embedded Contact homology = SW Floer homology (Taubes)
3) Gromov-Witten invariant = 4-dimensional SW-invariant (Taubes)
4) Turaev torsion = 3-dimensional SW-invariant (Turaev)
5) Milnor torsion (hence Alexander invariant) = 3-dimensional SW-invariant (Meng, Taubes)
6) Donaldson-Smith standard surface count = 4-dimensional SW-invariant (Usher)
7) Casson invariant (hence integral Theta divisor) = 3-dimensional SW-invariant (Lim)
8) Poincare Invariant = SW-invariant for algebraic surfaces (Okonek, et al.)
Conjectured:
8) Heegaard Floer closed 4-manifold invariant = SW-invariant (Ozsvath, Szabo)
*Analog of (1) above in dimension 4
9) Lagrangian matching invariant = SW-invariant (Perutz)
*Analog of (6) above for broken Lefschetz fibrations
10) Near-symplectic Gromov-Witten count = SW-invariant (Taubes)
*Analog of (4) above for near-symplectic manifolds, counting holomorphic curves in the complement of the degenerate circles of the near-symplectic form -- but this invariant hasn't really been defined yet
Does/should it stop there? Are there constructions out there that Seiberg-Witten Theory could possibly have a link with?

REPLY [7 votes]: Khovanov homology could probably fit into one of the two categories (although I'm not experienced enough to judge/guess whether it belongs to the "SW does it all" or to the "SW can't do it" category).
At a first glance, the two objects look quite different: Khovanov homology is a theory for knots and links in $S^3$ (and cobordisms between them), that categorifies the Jones polynomial, detects the unknot. It can be defined combinatorially in terms of knot diagrams, but I think that the original definition had a flavour of category theory and representation theory. However, Witten has recently proposed a gauge-theoretic approach to it, so maybe there's a deep connection after all.
Moreover, it's been known for some time that Khovanov homology and Heegaard Floer homology are related. Take a knot $K\subset S^3$: there's a spectral sequence, whose $E_2$-page is defined in terms of (a suitable variant of) $KhH(K)$, that converges to $\widehat{HF}(\Sigma(K))$, the Floer homology of the double cover of $S^3$, branched over $K$.