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A link invariant from the symplectic geometry of nilpotent slices

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 15 Sep 2006Embargo end date: 01 Jan 2004Publisher:Duke University PressJournal:Duke Mathematical Journal, volume 134 (issn: 0012-7094,

Authors: Seidel, Paul; Smith, Ivan;

doi: 10.1215/s0012-7094-06-13432-4 , 10.48550/arxiv.math/0405089

arXiv: http://arxiv.org/abs/math/0405089

A link invariant from the symplectic geometry of nilpotent slices

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Abstract

Using the symplectic geometry of certain manifolds which appear naturally in Lie theory, we define an invariant which assigns a graded abelian group to an oriented link. The relevant manifolds are transverse slices to certain nilpotent orbits inside sl_{2m}, and intersections of those with regular semisimple orbits. The invariant is conjectured to be equal to Khovanov's combinatorially defined homology theory (with the bigrading of that theory collapsed in a certain way).

v2: minor change to the introduction (grading in the long exact sequence corrected). v3: referees' suggestions and corrections incorporated; major changes to section 2 (the general Lie theory simplified by narrowing scope to sl_n) and minor changes to section 4 (more background on Floer theory included). This version to appear in Duke Mathematical Journal

Related Organizations

University of Chicago
United States
University of Cambridge
United Kingdom
Massachusetts Institute of Technology
United States
International Centre for Mathematical Sciences
United Kingdom

Keywords

14D05, 14D06, 53D40, Geometric Topology (math.GT), 17B45, Mathematics - Geometric Topology, Mathematics - Symplectic Geometry, 57M25, FOS: Mathematics, Symplectic Geometry (math.SG), Representation Theory (math.RT), 20C30, Mathematics - Representation Theory

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