The Equivariant Gromov-Witten theory of P**1

By A. Okounkov, R. Pandharipande. 2002

212 citations recorded by the source corpus.

We express all equivariant Gromov-Witten invariants of the projective line as matrix elements of explicit operators acting in the Fock space. As a consequence, we prove the equivariant theory is governed by the 2-Toda hierarchy of Ueno and Takasaki. This is the second in a sequence of three papers devoted to the Gromov-Witten theory of nonsingular target curves (the first paper of the series is math.AG/0204305).

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9d055d3404cbe50523b6c2e404414df4430cf42c

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Citations in the corpus

The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers (2009, background): “In recent years these equations have played an essential role in the study of Hurwitz numbers [24, 25, 34, 40, 41, 42].”
Virasoro constraints for target curves (2003, methodology): “In the second paper [ 12 ], we found an explicit operator formalism for the equivariant Gromov-Witten theory of P1 in terms of the infinite wedge representation.”
Hodge integrals and invariants of the unknot (2003, methodology): “Let Γ be a localization graph with nonvanishing contribution to the integral Ig,d(ν) with the specified lift: (i) The weight 0 linearization of O(−1) over 0 implies each vertex of Γ of 0 is of valence 1.”
A topological view of Gromov-Witten theory (2004, methodology): “The required Hodge integrals in the equivariant relative Gromov-Witten theory of P 1 are fully determined by the methods of the papers [3, 4, 17, 18 ].”
The Witten equation, mirror symmetry and quantum singularity theory (2007, methodology): “Those cases are 2-Toda for CP(1) by Okounkov-Pandharipande [OP06a] and the Virasoro constraints for toric manifolds by Givental [Giv01], and Riemann surfaces by Okounkov-Pandharipande [OP06b].”
Curves on K3 surfaces and modular forms (2010, background): “Faber and Pandharipande [13] describe how to replace Hodge insertions λj with descendent insertions, and the work of Okounkov and Pandharipande in [41], [ 42 ], [43] completely determines the descendent Gromov-Witten theory of target curves.”
The library of Babel: on the origin of gravitational thermodynamics (2005, background): “(11)Our limit shape (43) differs from the limit shapes of Young diagrams that appear in explicit instanton calculation in N = 2 super Yang-Mills theory [30] and in computations of certain GromovWitten invariants [31].”
Gromov-Witten theory, Hurwitz theory, and completed cycles (2002, unknown): “The special case, the GW/H correspondence for the absolute Gromov-Witten theory of P1, will be established by equivariant computations in [32].”
The Extended Toda Hierarchy (2003, result): “Probably, one can derive our Toda conjecture from the results of Okounkov and Pandharipande [27], [26] using the arguments of Getzler’s paper [16] along with the Givental’s result.”
The spaces of Laurent polynomials, Gromov-Witten theory of ℙ1-orbifolds and integrable hierarchies (2008, background): “— Equivariant quantum cohomology of CP AND the 2-Toda hierarchy ([29], [30]).”