Rational Quantum Cohomology of Steenrod Uniruled Manifolds

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.

12 pages

References in corpus (3)

• Punctured holomorphic curves and Lagrangian embeddings
• Covariant constancy of quantum Steenrod operations
• Homotopy type of the unitary group of the uniform Roe algebra on ${\mathbb{Z}}^n$