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A new cohomology theory of orbifold. (English) Zbl 1063.53091
The authors introduce the orbifold cohomology groups of an almost complex orbifold and the orbifold Dolbeault cohomology groups of a complex orbifold. The main result of the paper is the construction of orbifold cup products on orbifold cohomology groups and orbifold Dolbeault cohomology groups, which make the corresponding total orbifold cohomology into a ring with unity. Their considerations are motivated by the construction of the orbifold quantum cohomology groups.

MSC:
53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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