Volume 14, issue 1 (2014)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Computing Khovanov–Rozansky homology and defect fusion

Nils Carqueville and Daniel Murfet

Algebraic & Geometric Topology 14 (2014) 489–537
Abstract

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.

Keywords
adjunctions in bicategories, topological quantum field theories, matrix factorizations
Mathematical Subject Classification 2010
Primary: 18D05
Secondary: 57R56
References
Publication
Received: 11 December 2011
Revised: 1 June 2013
Accepted: 3 June 2013
Published: 23 January 2014
Authors
Nils Carqueville
Arnold 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
Daniel Murfet
Department of Mathematics
University of California, Los Angeles
520 Portola Plaza
Los Angeles, CA 90095
USA