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

Ruan, Yongbin; Tian, Gang

Math. Res. Lett. 1, No. 2, 269-278 (1994).

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)].

Reviewer: W.Kleinert (Berlin)

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)

Keywords:

two-dimensional topological quantum field theory; quantum cohomology; symplectic manifolds; algebraic curves; moduli spaces

Citations:

Zbl 0860.58005