Geometry & Topology

$\mathfrak{sl}(N)$–link homology ($N\geq 4$) using foams and the Kapustin–Li formula

Marco Mackaay, Marko Stošić, and Pedro Vaz

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Abstract

We use foams to give a topological construction of a rational link homology categorifying the sl(N) link invariant, for N4. To evaluate closed foams we use the Kapustin–Li formula adapted to foams by Khovanov and Rozansky [Adv. Theor. Math. Phys. 11 (2007) 233-259]. We show that for any link our homology is isomorphic to the Khovanov–Rozansky [Fund. Math. 199 (2008) 1-91] homology.

Article information

Source
Geom. Topol., Volume 13, Number 2 (2009), 1075-1128.

Dates
Received: 4 December 2007
Revised: 1 August 2008
Accepted: 31 December 2008
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800225

Digital Object Identifier
doi:10.2140/gt.2009.13.1075

Mathematical Reviews number (MathSciNet)
MR2491657

Zentralblatt MATH identifier
1202.57017

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 81R50: Quantum groups and related algebraic methods [See also 16T20, 17B37] 18G60: Other (co)homology theories [See also 19D55, 46L80, 58J20, 58J22]

Keywords
\mathfraksl(N) foams link homology Kapustin–Li Khovanov–Rozansky

Citation

Mackaay, Marco; Stošić, Marko; Vaz, Pedro. $\mathfrak{sl}(N)$–link homology ($N\geq 4$) using foams and the Kapustin–Li formula. Geom. Topol. 13 (2009), no. 2, 1075--1128. doi:10.2140/gt.2009.13.1075. https://projecteuclid.org/euclid.gt/1513800225


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