Let
be the cohomology of X modulo torsion. Define the small quantum cohomology with coefficients in Λ to be
Its elements are finite sums of the form
The small quantum cohomology is a graded R-module with
The ordinary cohomology H*(X) embeds into QH*(X, Λ) via, and QH*(X, Λ) is generated as a Λ-module by H*(X).
For any two cohomology classes a, b in H*(X) of pure degree, and for any A in, define (a∗b)A to be the unique element of H*(X) such that
(The right-hand side is a genus-0, 3-point Gromov-Witten invariant.) Then define
This extends by linearity to a well-defined Λ-bilinear map
called the small quantum cup product.
Read more about this topic: Quantum Cohomology
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