In the talk I will outline our (joint with Irit HuqKuruvilla) attempt to develop
the theory of GromovWitten invariants based on Euler characteristics rather than
intersection numbers. The purely homotopytheoretic aspects of the story begin with
the observation that in the category of stably almost complex manifolds the usual
Euler characteristic is bordisminvariant. This leads to the abstract cohomology
theory where the intersection of (stably almost complex) cycles is defined as the
Euler characteristic of their transverse intersection, and where the total Chern class
occurs in the role of the abstract Todd class. Our goal, however, is to apply this
idea in the context of GromovWitten (GW) theory.
In the talk I will outline the underlying philosophy and zoom in on some elementary
examples.
