Correlators and Descendants of Subcritical Stein Manifolds

TL;DR

This paper computes contact homology and related invariants for subcritical Stein-fillable contact manifolds with vanishing first Chern class, advancing understanding of their symplectic topology and algebraic properties.

Contribution

It provides explicit calculations of contact homology, genus-0 correlators, and gravitational descendants for subcritical Stein fillings, and relates these to the full potential function and algebraic structures.

Findings

Computed contact homology algebra for specific manifolds.

Determined the degree-2 differential in the Bourgeois--Oancea sequence.

Proved uniruledness of certain Kähler manifolds with subcritical polarization.

Abstract

We determine contact homology algebra of a subcritical Stein-fillable contact manifold whose first Chern class vanishes. We also compute the genus-0 one point correlators and gravitational descendants of compactly supported closed forms of their subcritical Stein fillings. This is a step towards determining the full potential function of the filling as defined in \cite{EliashbergGiventalHofer}. These invariants also give a canonical presentation of the cylindrical contact homology. With respect to this presentation, we determine the degree-2 differential in the Bourgeois--Oancea exact sequence of \cite{Oancea}. As a further application, we proved that if a K\"{a}hler manifold $M^{2n}$ admits a subcritical polarization and $c_1$ vanishes in the subcritical complement, then $M$ is uniruled.