The Toda conjecture
By E. Getzler. 2001
62 citations recorded by the source corpus.
We study the Toda conjecture of Eguchi and Yang for the Gromov-Witten invariants of CP^1,using the bihamiltonian method of the formal calculus of variations. We also study its relationship to the Virasoro conjecture for CP^1, recently proved by Givental (math.AG/0108100).
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1f4dba4fb63068bf8695ba17ff6b1e5dbfff8630
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In Geometry and Topology
- T. Milanov
- Boris Dubrovin
- Nick Scott
- You-jin Zhang
- Paul T. Norbury
- Guido Carlet
- E. Getzler
- R. Pandharipande
Citations in the corpus
- Gromov–Witten invariants of ℙ1 and Eynard–Orantin invariants (2011, background): “The Gromov–Witten invariants of P(1) have been studied and well understood over the last ten years (Getzler [12], and Okounkov and Pandharipande [16; 18; 17]).”
- Hirota quadratic equations for the extended Toda hierarchy (2005, methodology): “1In the papers [ Ge , Z] the ETH is defined implicitly via bihamiltonian recursion relations HIROTA QUADRATIC EQUATIONS FOR THE EXTENDED TODA HIERARCHY 3”
- The Extended Toda Hierarchy (2003, methodology): “Such an extension of the Toda lattice hierarchy is formulated independently in [15, 31], and the above conjecture is known to be true up to genus one approximation [5, 8, 11, 12, 13, 31].”
- Gromov-Witten theory, Hurwitz theory, and completed cycles (2002, unknown): “The Toda conjecture was further studied in in [6, 7, 16, 30, 34].”