Open topological recursion relations in genus $1$ and integrable systems

Abstract

The paper is devoted to the open topological recursion relations in genus 1, which are partial differential equations that conjecturally control open Gromov-Witten invariants in genus 1. We find an explicit formula for any solution analogous to the Dijkgraaf-Witten formula for a descendent Gromov-Witten potential in genus 1. We then prove that at the approximation up to genus 1 the exponent of an open descendent potential satisfies a system of explicitly constructed linear evolutionary PDEs with one spatial variable.

arXiv commentv4: correction of the spelling of the name of one of the authors, 12 pages

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• Gromov-Witten classes, quantum cohomology, and enumerative geometry
• Tautological relations and the r-spin Witten conjecture
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• On deformations of quasi-Miura transformations and the Dubrovin-Zhang bracket
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Cited by in corpus (1)

• A construction of open descendant potentials in all genera