Rational Quantum Cohomology of Steenrod Uniruled Manifolds

TL;DR

This paper demonstrates that Steenrod uniruled symplectic manifolds exhibit deformed quantum products, linking quantum Steenrod operations with rational Gromov-Witten theory and advancing understanding of the Chance-McDuff conjecture.

Contribution

It establishes a connection between Steenrod uniruledness and quantum product deformation, bridging recent advances in quantum Steenrod operations with Gromov-Witten theory.

Findings

Quantum Steenrod power differs from classical power in Steenrod uniruled manifolds.

Quantum product on such manifolds is deformed from the classical one.

Bridges the gap between Steenrod operations and Gromov-Witten invariants.

Abstract

We show that if a semipositive symplectic manifold $M^{2n}$ is Steenrod uniruled, in the sense that the quantum Steenrod power of the point class does not agree with its classical Steenrod power for any prime, then the (rational) quantum product on $M$ is deformed. This bridges the gap between the recent advances towards the Chance-McDuff conjecture utilizing quantum Steenrod operations, and the natural formulation of the Chance-McDuff conjecture in terms of rational Gromov-Witten theory.