Volume 8, issue 2 (2004)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Other MSP Journals
Hodge integrals and invariants of the unknot

Andrei Okounkov and Rahul Pandharipande

Geometry & Topology 8 (2004) 675–699
 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
Primary: 14H10
Secondary: 57M27