Title: Bordism of semi-free $S^1$-actions.
Author: Dev P. Sinha
AMS Class: 57R85 (primary); 55R40 (secondary).
LANL ID: math.AT/0303100
Addresses: Department of Mathematics, University of Oregon, Eugene OR
Email: dps@math.uoregon.edu
Abstract:
We calculate the geometric and homotopical (or stable) bordism rings associated
to semi-free $S^1$ actions on complex manifolds, giving explicit generators for
the geometric theory. To calculate the geometric theory, we prove a case of
the geometric realization conjecture, which in general would determine the
geometric theory in terms of the homotopical. The determination of
semi-free actions with isolated fixed points up to cobordism complements
similar results from symplectic geometry.