## Algebraic & Geometric Topology

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

#### Abstract

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

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

Dates
Revised: 5 November 2007
Accepted: 2 January 2008
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796815

Digital Object Identifier
doi:10.2140/agt.2008.8.309

Mathematical Reviews number (MathSciNet)
MR2443231

Zentralblatt MATH identifier
1159.57005

#### Citation

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. https://projecteuclid.org/euclid.agt/1513796815

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