The Quantum sl(N) Graph Invariant and a Moduli Space

Lobb, Andrew; Zentner, Raphael

doi:10.1093/imrn/rns275

The Quantum sl(N) Graph Invariant and a Moduli Space

Lobb, Andrew; Zentner, Raphael

Authors

Professor Andrew Lobb andrew.lobb@durham.ac.uk
Professor

Raphael Zentner

Abstract

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.

Citation

Lobb, A., & Zentner, R. (2013). The Quantum sl(N) Graph Invariant and a Moduli Space. International Mathematics Research Notices, Advance Access, https://doi.org/10.1093/imrn/rns275

Journal Article Type	Article
Publication Date	Jan 7, 2013
Deposit Date	Sep 19, 2013
Publicly Available Date	Feb 6, 2014
Journal	International Mathematics Research Notices
Print ISSN	1073-7928
Electronic ISSN	1687-0247
Publisher	Oxford University Press
Peer Reviewed	Peer Reviewed
Volume	Advance Access
DOI	https://doi.org/10.1093/imrn/rns275

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Copyright Statement
This is a pre-copyedited, author-produced PDF of an article accepted for publication in International mathematics research notices following peer review. The definitive publisher-authenticated version Lobb, A. and Zentner, R. (2013) 'The quantum sl(N) graph invariant and a moduli space.', International mathematics research notices, Advance Access is available online at: http://dx.doi.org/10.1093/imrn/rns275