The moduli space of maps
is highly singular, and yet it has a homology
class which behaves much like a fundamental class, and is hence called
the virtual fundamental class
defined in terms of the
deformation theory of stable maps to .
The Gromov-Witten
invariants of are defined by integrating various geometric cohomology
classes over this class.

Jeffrey Herschel Giansiracusa
2005-06-27