Nikita Markarian’s mathblog

On quantum cohomology

Posted in Mathematics by nikitamarkarian on May 5, 2010

Nowadays the theory of quantum cohomology is treated as a part of symplectic geometry. But it is not clear (for me) how much information about the symplectic structure does quantum cohomology contain. Perhaps, the situation is analagous to the Morse theory, where the definition is given in differential geometric terms (integral curves and so on) but the result is purely topological.

If one take as a starting point the paper of Witten and two papers of Givental (this and this), one may develop a theory of a different flavour sketched below. Conjecturally it coincides with the usual one, at least in some cases.