Algebraic & Geometric Topology

The foam and the matrix factorization $\mathit{sl}_3$ link homologies are equivalent

Marco Mackaay and Pedro Vaz

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We prove that the universal rational sl3 link homologies which were constructed by Khovanov in [?] and the authors in [?], using foams, and by Khovanov and Rozansky in [?], using matrix factorizations, are naturally isomorphic as projective functors from the category of links and link cobordisms to the category of bigraded vector spaces.

Article information

Algebr. Geom. Topol., Volume 8, Number 1 (2008), 309-342.

Received: 16 October 2007
Revised: 5 November 2007
Accepted: 2 January 2008
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 Khovanov–Rozansky link homology matrix factorization


Mackaay, Marco; Vaz, Pedro. The foam and the matrix factorization $\mathit{sl}_3$ link homologies are equivalent. Algebr. Geom. Topol. 8 (2008), no. 1, 309--342. doi:10.2140/agt.2008.8.309.

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