Geometry & Topology 8 (2004) 675–699

DOI: 10.2140/gt.2004.8.675

arXiv: math.AG/0307209

Abstract

We prove the Gopakumar–Mariño–Vafa formula for special cubic Hodge integrals. The GMV formula arises from Chern–Simons/string duality applied to the unknot in the three sphere. The GMV formula is a q–analog of the ELSV formula for linear Hodge integrals. We find a system of bilinear localization equations relating linear and special cubic Hodge integrals. The GMV formula then follows easily from the ELSV formula. An operator form of the GMV formula is presented in the last section of the paper.

Keywords

Hodge integrals, unknot, Gopakumar–Mariño–Vafa formula

Mathematical Subject Classification

Primary: 14H10

Secondary: 57M27

References

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Publication

Received: 30 September 2003
Revised: 22 April 2004
Accepted: 13
Published: 24 April 2004
Proposed: Robion Kirby
Seconded: Shigeyuki Morita, Ralph Cohen

Authors