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The moduli problem of Lobb and Zentner and the coloured sl(N) graph invariant

Grant, Jonathan

The moduli problem of Lobb and Zentner and the coloured sl(N) graph invariant Thumbnail


Authors

Jonathan Grant



Abstract

Motivated by a possible connection between the SU(N) instanton knot Floer homology of Kronheimer and Mrowka and sl(N) Khovanov-Rozansky homology, Lobb and Zentner recently introduced a moduli problem associated to colourings of trivalent graphs of the kind considered by Murakami, Ohtsuki and Yamada in their state-sum interpretation of the quantum sl(N) knot polynomial. For graphs with two colours, they showed this moduli space can be thought of as a representation variety, and that its Euler characteristic is equal to the sl(N) polynomial of the graph evaluated at 1. We extend their results to graphs with arbitrary colourings by irreducible anti-symmetric representations of sl(N).

Citation

Grant, J. (2013). The moduli problem of Lobb and Zentner and the coloured sl(N) graph invariant. Journal of Knot Theory and Its Ramifications, 22(10), https://doi.org/10.1142/s0218216513500600

Journal Article Type Article
Publication Date Oct 1, 2013
Deposit Date Dec 4, 2013
Publicly Available Date Jan 24, 2014
Journal Journal of Knot Theory and Its Ramifications
Print ISSN 0218-2165
Electronic ISSN 1793-6527
Publisher World Scientific Publishing
Peer Reviewed Peer Reviewed
Volume 22
Issue 10
DOI https://doi.org/10.1142/s0218216513500600
Keywords Moduli problem, MOY graph invariant, Colored graph, Representation variety.

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