Ellipsoidal superpotentials and stationary descendants

TL;DR

This paper develops methods to compute punctured curve counts in symplectic ellipsoids, introduces recursive formulas, and explores elementary symplectic cobordisms, advancing understanding in symplectic geometry.

Contribution

It introduces a framework for explicit punctured curve count computations and initiates the study of infinitesimal symplectic cobordisms between ellipsoids.

Findings

Derived new recursive formulas for punctured curve counts

Developed a framework for explicit computations using standard complex structures

Initiated the study of elementary symplectic cobordisms

Abstract

We compute stationary gravitational descendants in symplectic ellipsoids of any dimension, and use these to derive a number of new recursive formula for punctured curve counts in symplectic manifolds with ellipsoidal ends. Along the way we develop a framework in which punctured curve counts can be explicitly computed using the standard complex structure on affine space. Finally, we initiate the study of "infinitesimal symplectic cobordisms", which serve as elementary building blocks for symplectic cobordisms between ellipsoids.