Gravitational Descendants and Linearized Contact Homology

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