Computations of Complex Equivariant Bordism Rings
by
Dev Sinha
Mathematics Department
Box 1917
Brown University
Providence, RI 02912
E-mail: dps@math.brown.edu
This paper is a significantly revised version of a previous submission to
the Hopf archive.
In this paper we compute homotopical bordism rings $MU^G_*$ for abelian
compact Lie groups G, giving explicit generators and relations.
The key constructions are operations on equivariant bordism which should
play an important role in equivariant stable homotopy theory more
generally. The main technique used is localization of the theory
by inverting Euler classes. Applications to homotopy theory
include analysis of the completion map from $MU^G_*$ to $MU^*(BG)$.
Applications to geometry include classification
up to cobordism of $S^1$ actions on stably complex four-manifolds with
precisely three fixed points, answering a question of Bott.