The jet-space of a Frobenius manifold and higher-genus Gromov-Witten invariants
By E. Getzler. 2002
50 citations recorded by the source corpus.
The theory of genus zero Gromov-Witten invariants associates to a compact symplectic manifold X a Frobenius manifold H (also known as the small phase space of X) whose underlying flat manifold is the cohomology space H*(X, ℂ). Higher genus Gromov-Witten invariants give rise to a sequence of generating functions F g X , one for each genus g > 0; these are functions on the large phase space $${H_{\infty }} = {H^{*}}\left( {X \times \mathbb{C}{mathbb{P}^{\infty }},\mathbb{C}} \right)$$ The manifold H∞ has a rich geometric structure: it is the jet space of curves in the Frobenius manifold H. (This identification is implicit in Dubrovin [9].)
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1396e84ab65f2e04c64c9597ad02d161225a6a28
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In Geometry and Topology
- Y.-P. Lee
- Alexander Givental
- Sergey Shadrin
- H. Iritani
- C. Teleman
- T. Milanov
- Valentin Tonita
- Hsian-Hua Tseng
In Mathematical Physics
- Y.-P. Lee
- Alexander Givental
- Sergey Shadrin
- T. Milanov
- C. Teleman
- H. Iritani
- Hsian-Hua Tseng
- Valentin Tonita
Citations in the corpus
- GROMOV - WITTEN INVARIANTS AND QUANTIZATION OF QUADRATIC HAMILTONIANS (2001, methodology): “Moreover, using these results, Getzler [15] proves the 3g − 2-jet conjecture of Eguchi – Xiong and Dubrovin about genus g descendent potential FgX (we are not going to formulate it here — see [13] for details) by showing that it is equivalent to the following property of the genus g ancestor potenti”
- Invariance of tautological equations II: Gromov-Witten theory (2006, background): “It was discovered in [11], following the works in [15] and [10], that A := Ŝsτ is the corresponding generating function for “ancestors”.”