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Abstract |
Abstract: 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.
The plan for the talk includes three elements: (i) some preliminaries on complex
cobordisms, (ii) the thick-brush overview of why the Chern-Euler GW-theory might
be interesting, and (iii) a simplest example dealing with the Euler
characteristics of Deligne-Mumford spaces factorized by permutations of marked
points. |
