Algebraic & Geometric Topology

Computing Khovanov–Rozansky homology and defect fusion

Nils Carqueville and Daniel Murfet

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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.

Article information

Algebr. Geom. Topol., Volume 14, Number 1 (2014), 489-537.

Received: 11 December 2011
Revised: 1 June 2013
Accepted: 3 June 2013
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 18D05: Double categories, 2-categories, bicategories and generalizations
Secondary: 57R56: Topological quantum field theories

adjunctions in bicategories topological quantum field theories matrix factorizations


Carqueville, Nils; Murfet, Daniel. Computing Khovanov–Rozansky homology and defect fusion. Algebr. Geom. Topol. 14 (2014), no. 1, 489--537. doi:10.2140/agt.2014.14.489.

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