Jonathan Grant
The moduli problem of Lobb and Zentner and the coloured sl(N) graph invariant
Grant, Jonathan
Authors
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. |
Public URL | https://durham-repository.worktribe.com/output/1443687 |
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Copyright Statement
Electronic version of an article published as Journal of knot theory and its ramifications, 22, 1350060, 2013, 10.1142/S0218216513500600, © World Scientific Publishing Company, http://www.worldscientific.com/worldscinet/jktr
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