The quantum Euler class and the quantum cohomology of the Grassmannians

DOI10.1007/BF02773576zbMath0954.53048arXivq-alg/9712025MaRDI QIDQ1567350

Lowell Abrams

Publication date: 24 July 2000

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9712025

zbMATH Keywords

symplectic manifoldFrobenius algebracharacteristic elementdegree \(d\) hypersurfacesLandau-Ginzberg potential

Mathematics Subject Classification ID

Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of global analysis to structures on manifolds (57R57) Gromov-Witten invariants, quantum cohomology, Frobenius manifolds (53D45)

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Cites Work

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• On quantum cohomology rings of Fano manifolds and a formula of Vafa and Intriligator
• Supersymmetry and Morse theory
• Gromov-Witten classes, quantum cohomology, and enumerative geometry
• Morse Theory. (AM-51)
• Characteristic Classes. (AM-76)
• TOWARDS A SCHUBERT CALCULUS FOR MAPS FROM A RIEMANN SURFACE TO A GRASSMANNIAN
• Intersection theory on \overline{ℳ}_{1,4} and elliptic Gromov-Witten invariants
• TWO-DIMENSIONAL TOPOLOGICAL QUANTUM FIELD THEORIES AND FROBENIUS ALGEBRAS
• Quantum Cohomology of Rational Surfaces
• Direct sum decompositions and indecomposable TQFTs
• A mathematical theory of quantum cohomology