Hodge integrals and invariants of the unknot

By A. Okounkov, R. Pandharipande. 2003

102 citations recorded by the source corpus.

We prove the Gopakumar{Mari~ no{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 nd 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. AMS Classication numbers Primary: 14H10 Secondary: 57M27

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/5ae718f64535a301f1e37aa00043ea7e9e4471ff

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Nuclear and High Energy Physics

Citations in the corpus

The local Gromov-Witten theory of curves (2004, background): “Consider a degeneration of X to X1∪B X2, the union of X1 and X2 along a smooth divisor B.”
Quantum Calabi-Yau and Classical Crystals (2003, background): “For some mathematical aspects of the topological vertex, see [8, 9, 3].”
A mathematical theory of the topological vertex (2004, background): “The main result of [30] is the following formula conjectured by Mariño and Vafa [33] (see [40] for another proof): Theorem 8.”
Chern-Simons theory and topological strings (2004, unknown): “It has been rigorously proved by Liu, Liu, and Zhou (2003a) and by Okounkov and Pandharipande (2004), and shown to have many applications in Gromov-Witten theory (Liu, Liu and Zhou, 2003b; Zhou, 2003).”
The local Donaldson–Thomas theory of curves (2005, unknown): “The 1–legged equivariant vertex (ii) contains the Calabi–Yau 1–legged vertex governed by the Gopakumar–Mariño–Vafa formula (see Liu–Liu–Zhou [21], Mariño–Vafa [23] and Okounkov–Pandharipande [29]) as a special case.”
Matrix models, geometric engineering and elliptic genera (2003, background): “a T2 ﬁbration over the plane. Along each edge of the web a 1-cycle of the ﬁber T2 shrinks and therefore at each point 5The relation between Hodge integrals and topological vertex was also explored in [65,66,67,68,69,70] 42 of the edge we have an S1, the cycle dual to the one shrinking. Given this cy”
Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds (2008, background): “The 1-leg version of the topological vertex appeared first in [21] and was proven in [19, 28 ].”
A Proof of a Conjecture of Marino-Vafa on Hodge Integrals (2003, background): “Initial Condition The proof of the initial condition (b) needs the following two theorems.”