Open topological recursion relations in genus $1$ and integrable systems
Mathematical Physics
2021-07-14 v4 Algebraic Geometry
math.MP
Symplectic Geometry
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.
Cite
@article{arxiv.2008.06922,
title = {Open topological recursion relations in genus $1$ and integrable systems},
author = {Oscar Brauer and Alexandr Buryak},
journal= {arXiv preprint arXiv:2008.06922},
year = {2021}
}
Comments
v4: correction of the spelling of the name of one of the authors, 12 pages