Mathematics – Algebraic Geometry
Scientific paper
2005-02-20
Geom. Topol. Monogr. 8 (2006) 105-128
Mathematics
Algebraic Geometry
This is the version published by Geometry & Topology Monographs on 22 April 2006
Scientific paper
10.2140/gtm.2006.8.105
Based on the duality between open-string theory on noncompact Calabi-Yau threefolds and Chern-Simons theory on three manifolds, M Marino and C Vafa conjectured a formula of one-partition Hodge integrals in term of invariants of the unknot (hep-th/0108064). Many Hodge integral identities, including the lambda_g conjecture and the ELSV formula, can be obtained by taking limits of the Marino-Vafa formula. Motivated by the Marino-Vafa formula and formula of Gromov-Witten invariants of local toric Calabi-Yau threefolds predicted by physicists, J Zhou conjectured a formula of two-partition Hodge integrals in terms of invariants of the Hopf link (math.AG/0310282) and used it to justify physicists' predictions (math.AG/0310283). In this expository article, we describe proofs and applications of these two formulae of Hodge integrals based on joint works of K Liu, J Zhou and the author (math.AG/0306257, math.AG/0306434, math.AG/0308015, math.AG/0310272). This is an expansion of the author's talk of the same title at the BIRS workshop: "The Interaction of Finite Type and Gromov-Witten Invariants", November 15--20, 2003.
No associations
LandOfFree
Formulae of one-partition and two-partition Hodge integrals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Formulae of one-partition and two-partition Hodge integrals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Formulae of one-partition and two-partition Hodge integrals will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-197669