Gromov-Witten Invariants of Blow-ups Along Points and Curces

TL;DR

This paper investigates how Gromov-Witten invariants change when a symplectic manifold is blown up at points or along curves, using the gluing formula to establish relations between invariants of the original and the blown-up manifold.

Contribution

It introduces new relations between Gromov-Witten invariants of a manifold and its blow-ups at points or curves, utilizing the gluing formula of Li and Ruan.

Findings

Established relations between invariants of M and its blow-ups

Applied symplectic cutting and gluing formula techniques

Extended understanding of Gromov-Witten invariants in blow-up scenarios

Abstract

In this paper, using the gluing formula of Gromov-Witten invariants under symplectic cutting, due to Li and Ruan, we studied the Gromov-Witten invariants of blow-ups at a smooth point or along a smooth curve. We established some relations between Gromov-Witten invariants of M and its blow-ups at a smooth point or along a smooth curve.