The foam and the matrix factorization sl3 link homologies are equivalent

Mackaay, Marco; Vaz, Pedro

doi:10.2140/agt.2008.8.309

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

Marco Mackaay and Pedro Vaz

Algebraic & Geometric Topology 8 (2008) 309–342

DOI: 10.2140/agt.2008.8.309

Abstract

We prove that the universal rational ${s l}_{3}$ 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.

Keywords

$sl_3$, foams, Khovanov, Khovanov–Rozansky, link homology, matrix factorization

Mathematical Subject Classification 2000

Primary: 57M27

Secondary: 57M25, 81R50, 18G60

References

Publication

Received: 16 October 2007

Revised: 5 November 2007

Accepted: 2 January 2008

Published: 12 March 2008

Authors

Marco Mackaay
Departamento de Matemática Universidade do Algarve Campus de Gambelas 8005-139 Faro Portugal

Pedro Vaz
Departamento de Matemática Universidade do Algarve Campus de Gambelas 8005-139 Faro Portugal

Volume 8, issue 1 (2008)