Dubrovin Connection
When the base ring R is C, one can view the evenly-graded part H of the vector space QH*(X, Λ) as a complex manifold. The small quantum cup product restricts to a well-defined, commutative product on H. Under mild assumptions, H with the intersection pairing is then a Frobenius algebra.
The quantum cup product can be viewed as a connection on the tangent bundle TH, called the Dubrovin connection. Commutativity and associativity of the quantum cup product then correspond to zero-torsion and zero-curvature conditions on this connection.
Read more about this topic: Quantum Cohomology
Famous quotes containing the word connection:
“It may comfort you to know that if your child reaches the age of eleven or twelve and you have a good bond or relationship, no matter how dramatic adolescence becomes, you children will probably turn out all right and want some form of connection to you in adulthood.”
—Charlotte Davis Kasl (20th century)