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A link invariant from the symplectic geometry of nilpotent slices. (English) Zbl 1108.57011

The authors define a link invariant by using symplectic geometry and conjecture that this invariant coincides with the collapsed Khovanov homology.
As it is well known, a link can be regarded as the closure of a braid due to J. W. Alexander [Proc. Nat. Acad. Sci. USA 9, 93–95 (1923; JFM 49.0408.03)]. Markov’s theorem says that two braids give the same link if and only if they are related by conjugations and stabilizations [A. Markoff, Rec. Math. Moscou, n. Ser. 1, 73–78 (1936; Zbl 0014.04202)].
The authors regard a braid as a loop in the unordered configuration space \(\text{Conf}_{n}(\mathbb{C}):= \{(\mu_{1},\mu_{2},\dots,\mu_{n})\in\mathbb{C}^{n}\mid \text{}\mu_{i}\neq\mu_{j}\) if \(i\neq j\)

MSC:

57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
57R58 Floer homology
57M25 Knots and links in the \(3\)-sphere (MSC2010)
20F36 Braid groups; Artin groups
53D40 Symplectic aspects of Floer homology and cohomology
17B45 Lie algebras of linear algebraic groups
14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
14D06 Fibrations, degenerations in algebraic geometry
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References:

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