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A mathematical theory of quantum cohomology. (English) Zbl 0860.58006

This article provides both a brief survey and an announcement of the main results of the authors’ subsequent, comprehensive and detailed treatise under the same title [J. Differ. Geom. 42, No. 2, 259–367 (1995; Zbl 0860.58005 above)].

MSC:

58D27 Moduli problems for differential geometric structures
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
14H15 Families, moduli of curves (analytic)
58D15 Manifolds of mappings
14N10 Enumerative problems (combinatorial problems) in algebraic geometry
81T45 Topological field theories in quantum mechanics
14F45 Topological properties in algebraic geometry
14H10 Families, moduli of curves (algebraic)
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
57R56 Topological quantum field theories (aspects of differential topology)

Citations:

Zbl 0860.58005
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