Hodge integrals and invariants of the unknot

Okounkov, Andrei¹ ; Pandharipande, Rahul¹

¹ Department of Mathematics, Princeton University, Princeton, New Jersey 08544, USA

Geometry & topology, Tome 8 (2004) no. 2, pp. 675-699.

Résumé

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.

Détail

DOI : 10.2140/gt.2004.8.675

Keywords: Hodge integrals, unknot, Gopakumar–Mariño–Vafa formula

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