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The Moduli Problem of Lobb and Zentner and the Coloured sl(N) Graph Invariant | | Jonathan Grant
; | | Date: |
18 Dec 2012 | | Abstract: | Motivated by a possible connection between the $mathrm{SU}(N)$ instanton
knot Floer homology of Kronheimer and Mrowka and $mathfrak{sl}(N)$
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
$mathfrak{sl}(N)$ 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 $mathfrak{sl}(N)$ polynomial of the graph
evaluated at 1. We extend their results to graphs with arbitrary colourings by
irreducible anti-symmetric representations of $mathfrak{sl}(N)$. | | Source: | arXiv, 1212.4511 | | Services: | Forum | Review | PDF | Favorites | |
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