Gravitational Descendants and Linearized Contact Homology

TL;DR

This paper establishes a recursion relation linking gravitational descendants in Stein domains to linearized contact homology, enabling reduction to Gromov--Witten invariants through a degree -2 map.

Contribution

It introduces a new recursion relation connecting gravitational descendants with linearized contact homology using the map D.

Findings

Recursion relation between gravitational descendants and contact homology.

Reduction of gravitational descendants to Gromov--Witten invariants.

Identification of the degree -2 map D in the Bourgeois--Oancea sequence.

Abstract

In this paper we prove a recursion relation between the the one-point genus-0 gravitational descendants of a Stein domain $(M,\partial M)$. This relation is best described by the degree -2 map $D$ in the linearized contact homology of $\partial M$, arising from the Bourgeois--Oancea exact sequence between symplectic homology of $M$ and linearized contact homology of $\partial M$. All one-point genus-0 gravitational descendants can be reduce to the one-point Gromov--Witten invariants via iterates of $D$.