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On the computation of torus link homology

Part of: Low-dimensional topology

Published online by Cambridge University Press:  23 November 2018

Ben Elias  and
Matthew Hogancamp
Ben Elias
Affiliation:
Department of Mathematics, Fenton Hall, University of Oregon, Eugene, OR 97403, USA email belias@uoregon.edu
Matthew Hogancamp
Affiliation:
Department of Mathematics, Indiana University, 831 East 3rd St. Bloomington, IN 47405, USA email hogancam@usc.edu
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Abstract

We introduce a new method for computing triply graded link homology, which is particularly well adapted to torus links. Our main application is to the $(n,n)$-torus links, for which we give an exact answer for all $n$. In several cases, our computations verify conjectures of Gorsky et al. relating homology of torus links with Hilbert schemes.

Keywords

Khovanov–Rozansky homologySoergel bimodulestorus links

MSC classification

Primary: 57M27: Invariants of knots and 3-manifolds
Type
Research Article
Information
Compositio Mathematica , Volume 155 , Issue 1 , January 2019 , pp. 164 - 205
Copyright
© The Authors 2018 

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Footnotes

1

Current address: Department of Mathematics, University of Southern California, 3620 S. Vermont Ave., KAP 104 Los Angeles, CA 90089, USA

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