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Rational Quantum Cohomology of Steenrod Uniruled Manifolds

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arxiv 2111.09157 v1 pith:UBJWTCVA submitted 2021-11-16 math.SG

Semon Rezchikov This is my paper · ORCID
classification math.SG
keywords steenrodquantumrationalchance-mcduffconjecturepoweruniruledadvances
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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.

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  1. Quantum Steenrod powers and Hamiltonian maps

    math.SG 2026-07 conditional novelty 7.0 of 10

    Hamiltonian pseudo-rotations and finite-order Hamiltonian diffeomorphisms force geometric uniruledness; new criteria (non-torsion orbits, symplectically degenerate maxima, reversed Hofer–Zehnder) force infinitely many...

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