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Link homology theories from symplectic geometry

Name: Link homology theories from symplectic geometry
Creator: Ciprian Manolescu
Keywords: Knots, Mathematics(all), Khovanov–Rozansky homology, 53D40, Geometric Topology (math.GT), 01 natural sciences, Floer homology, 53D40; 57R58, Mathematics - Geometric Topology, Mathematics - Symplectic Geometry

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 May 2007Embargo end date: 01 Jan 2006Publisher:Elsevier BVJournal:Advances in Mathematics, volume 211, pages 363-416 (issn: 0001-8708,

Authors: Ciprian Manolescu;

doi: 10.1016/j.aim.2006.09.007 , 10.48550/arxiv.math/0601629

arXiv: http://arxiv.org/abs/math/0601629

Link homology theories from symplectic geometry

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Abstract

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

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Keywords

Knots, Mathematics(all), Khovanov–Rozansky homology, 53D40, Geometric Topology (math.GT), Floer homology, 53D40; 57R58, Mathematics - Geometric Topology, Mathematics - Symplectic Geometry, FOS: Mathematics, Symplectic Geometry (math.SG), 57R58, Links

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