Covariant constancy of quantum Steenrod operations

Abstract

We prove a relationship between quantum Steenrod operations and the quantum connection. In particular there are operations extending the quantum Steenrod power operations that, when viewed as endomorphisms of equivariant quantum cohomology, are covariantly constant. We demonstrate how this property is used in computations of examples.

arXiv comment36 pages, 5 figures. Small changes to exposition, and correction of typos. To appear in the volume in honour of Claude Viterbo's sixtieth birthday in JFPTA, 2022. "This version of the article has been accepted for publication, after peer review, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections." DOI:10.1007/s11784-022-00967-4

References in corpus (3)

• Rational curves on hypersurfaces [after A. Givental]
• A construction of the quantum Steenrod squares and their algebraic relations
• Formal groups and quantum cohomology

Cited by in corpus (5)

• Formal groups and quantum cohomology
• Flat endomorphisms for mod $p$ equivariant quantum connections from quantum Steenrod operations
• Quantum Steenrod operations of symplectic resolutions
• The $\mathbb{Z}/p$-equivariant cohomology of genus zero Deligne-Mumford space with $1+p$ marked points
• Rational Quantum Cohomology of Steenrod Uniruled Manifolds