The quantum sl(n) graph invariant and a moduli space

Details The quantum sl(n) graph invariant and a moduli space The quantum sl(n) graph invariant and a moduli space

2012-04-24

arxiv.org/abs/1204.5372v1

Mathematics

Geometric Topology

13 pages, 7 figures

Scientific paper

We associate a moduli problem to a colored trivalent graph; such graphs, when planar, appear in the state-sum description of the quantum sl(N) knot polynomial due to Murakami, Ohtsuki, and Yamada. We discuss how the resulting moduli space can be thought of a representation variety. We show that the Euler characteristic of the moduli space is equal to the quantum sl(N) polynomial of the graph evaluated at unity. Possible extensions of the result are also indicated.

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