Algebraic & Geometric Topology

The universal $sl_3$–link homology

Marco Mackaay and Pedro Vaz

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We define the universal sl3–link homology, which depends on 3 parameters, following Khovanov’s approach with foams. We show that this 3–parameter link homology, when taken with complex coefficients, can be divided into 3 isomorphism classes. The first class is the one to which Khovanov’s original sl3–link homology belongs, the second is the one studied by Gornik in the context of matrix factorizations and the last one is new. Following an approach similar to Gornik’s we show that this new link homology can be described in terms of Khovanov’s original sl2–link homology.

Article information

Algebr. Geom. Topol., Volume 7, Number 3 (2007), 1135-1169.

Received: 8 May 2007
Accepted: 30 May 2007
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

$sl_3$ foams Khovanov link homology


Mackaay, Marco; Vaz, Pedro. The universal $sl_3$–link homology. Algebr. Geom. Topol. 7 (2007), no. 3, 1135--1169. doi:10.2140/agt.2007.7.1135.

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