Link homology theories from symplectic geometry
Copyright policy )Link homology theories from symplectic geometry
For each positive integer n, Khovanov and Rozansky constructed an invariant of links in the form of a doubly-graded cohomology theory whose Euler characteristic is the sl(n) link polynomial. We use Lagrangian Floer cohomology on some suitable affine varieties to build a similar series of link invariants, and we conjecture them to be equal to those of Khovanov and Rozansky after a collapsation of the bigrading. Our work is a generalization of that of Seidel and Smith, who treated the case n=2.
47 pages, 6 figures; revised version
- Columbia University United States
- King’s University United States
- Department of Mathematics Columbia University United States
- Columbia University United States
- Columbia University United States
Knots, Mathematics(all), link, Khovanov–Rozansky homology, 53D40, Geometric Topology (math.GT), Invariants of knots and \(3\)-manifolds, Floer homology, 53D40; 57R58, Global theory of symplectic and contact manifolds, Khovanov-Rozansky homology, Mathematics - Geometric Topology, Mathematics - Symplectic Geometry, knot, FOS: Mathematics, Symplectic Geometry (math.SG), 57R58, Links, link homology
Knots, Mathematics(all), link, Khovanov–Rozansky homology, 53D40, Geometric Topology (math.GT), Invariants of knots and \(3\)-manifolds, Floer homology, 53D40; 57R58, Global theory of symplectic and contact manifolds, Khovanov-Rozansky homology, Mathematics - Geometric Topology, Mathematics - Symplectic Geometry, knot, FOS: Mathematics, Symplectic Geometry (math.SG), 57R58, Links, link homology
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).11 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!