Computing Khovanov–Rozansky homology and defect fusion

Carqueville, Nils; Murfet, Daniel

doi:10.2140/agt.2014.14.489

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Computing Khovanov–Rozansky homology and defect fusion

Nils Carqueville and Daniel Murfet

Algebraic & Geometric Topology 14 (2014) 489–537

DOI: 10.2140/agt.2014.14.489

Abstract

We compute the categorified $s l (N)$ 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

Volume 14, issue 1 (2014)