Seminar in Real and Complex Geometry

Thursday, June 15, 2023, 17:15-18:45, online via zoom

Alexander Givental
(University of California Berkeley)

Chern-Euler intersection theory and Gromov-Witten invariants


In the talk I will outline our (joint with Irit Huq-Kuruvilla) attempt to develop the theory of Gromov-Witten invariants based on Euler characteristics rather than intersection numbers. The purely homotopy-theoretic aspects of the story begin with the observation that in the category of stably almost complex manifolds the usual Euler characteristic is bordism-invariant. 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 Gromov-Witten (GW) theory. In the talk I will outline the underlying philosophy and zoom in on some elementary examples.