Computing Khovanov–Rozansky homology and defect fusion

Carqueville, Nils¹ ; Murfet, Daniel²

¹Arnold Sommerfeld Center for Theoretical Physics, LMU München, Theresienstr. 37, 80333 München, Germany, and, Excellence Cluster Universe, Technische Universität München, Boltzmannstr. 2, D-85748 Garching, Germany
²Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, CA 90095, USA

Algebraic and Geometric Topology, Tome 14 (2014) no. 1, pp. 489-537

Résumé

We compute the categorified sl(N) link invariants as defined by Khovanov and Rozansky, for various links and values of N. This is made tractable by an algorithm for reducing tensor products of matrix factorizations to finite rank, which we implement in the computer algebra package Singular.

Détail

DOI : 10.2140/agt.2014.14.489

Classification : 18D05, 57R56
Keywords: adjunctions in bicategories, topological quantum field theories, matrix factorizations

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