Quantum cohomology

From Talbot

This should be a gentle introduction to quantum cohomology. It needs to cover virtual dimensions of the space of holomorphic spheres, the definition of the 3-point invariant, a sketch of the proof of associativity, and the example of complex projective space.

I would propose to try an interpretation of the Floer cohomology of RP_n \subset CP_n with its product structure as a real analogue. We use Z/2 coefficients for simplicity: additively, the Floer cohomology is the ordinary cohomology (see Oh's classical papers), but the multiplicative structure is deformed by contributions from holomorphic discs, which are counted in analogy with CP_n. This can be done "experimentally", referring to the later talk for more systematic results.

Note Z/2 coefficients are important: the Floer cohomology of (RP_3, RP_3) with rational coefficients is trivial (easy to see due to its structure as a module over quantum cohomology, by the way).