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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
$\mathfrak{sl}(N)$–link homology ($N\geq 4$) using foams and the Kapustin–Li formula

Marco Mackaay, Marko Stošić and Pedro Vaz

Geometry & Topology 13 (2009) 1075–1128
Abstract

We use foams to give a topological construction of a rational link homology categorifying the sl(N) link invariant, for N 4. 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.

Keywords
\mathfraksl(N), foams, link homology, Kapustin–Li, Khovanov–Rozansky
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57M25, 81R50, 18G60
References
Publication
Received: 4 December 2007
Revised: 1 August 2008
Accepted: 31 December 2008
Published: 27 January 2009
Proposed: Peter Ozsváth
Seconded: Peter Teichner, Robion Kirby
Authors
Marco Mackaay
Departamento de Matemática
Universidade do Algarve
Campus de Gambelas
8005-139 Faro
Portugal
Marko Stošić
Instituto de Sistemas e Robótica and CAMGSD
Instituto Superior Técnico
Avenida Rovisco Pais
1049-001 Lisboa
Portugal
Pedro Vaz
Departamento de Matemática
Universidade do Algarve
Campus de Gambelas
8005-139 Faro
Portugal