Quantum Cohomology of a Product

Abstract

The operation of tensor product of Cohomological Field Theories (or algebras over genus zero moduli operad) introduced in an earlier paper by the authors is described in full detail, and the proof of a theorem on additive relations between strata classes is given. This operation is a version of the Kuenneth formula for quantum cohomology. In addition, rank one CohFT's are studied, and a generalization of Zograf's formula for Weil-Petersson volumes is suggested.

AMSTex file, 30 pages. Figures (hard copies) available from Yu. Manin. Main paper by M. Kontsevich, Yu. Manin, appendix by R. Kaufmann

References in corpus (3)

• Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves
• Geometry of 2d topological field theories
• Quantum intersection rings

Cited by in corpus (25)

• A descendent relation in genus 2
• Quantum K-theory of Grassmannians
• The product formula for Gromov-Witten invariants
• Higher Weil-Petersson Volumes of Moduli Spaces of Stable $n$-pointed Curves
• Structures in higher-dimensional category theory
• The Log Product Formula
• Generalized Enrichment for Categories and Multicategories
• Hilbert-Poincaré series of matroid Chow rings and intersection cohomology
• The Liouville Geometry of N=2 Instantons and the Moduli of Punctured Spheres
• Painleve' transcendents and two-dimensional topological field theory
• Nonperturbative Model Of Liouville Gravity
• Multi-Instanton Measure from Recursion Relations in N=2 Supersymmetric Yang-Mills Theory
• Frobenius manifolds and Frobenius algebra-valued integrable systems
• Residual categories for (co)adjoint Grassmannians in classical types
• The pre-WDVV ring of physics and its topology
• Stable Spin Maps, Gromov-Witten Invariants, and Quantum Cohomology
• The Instanton Universal Moduli Space of N=2 Supersymmetric Yang-Mills Theory
• The Log Product Formula in quantum $K$-theory
• New moduli spaces of pointed curves and pencils of flat connections
• Enumerative and asymptotic analysis of a moduli space
• Gromov-Witten theory with derived algebraic geometry
• The Chow ring of Mbar_{0,m}(n, d)
• Non-trivial 1-classes in the homology of the real moduli spaces M-bar_{0,n} and related structures
• A Product Formula for Gromov-Witten Invariants
• Moduli Spaces and Multiple Polylogarithm Motives