Computations in Complex Equivariant Bordism Theory
by
Dev Sinha
Mathematics Department
Box 1917
Brown University
Providence, RI 02912
E-mail: dps@math.brown.edu
In this paper we present computations of the ring structure of the
coefficients of equivariant bordism, answering questions which have been open
since these theories were first defined by Conner and Floyd and tom Dieck.
We have a result which establishes an algebraic framework in which to
understand equivariant bordism for any group such that any proper subgroup is
contained in a proper normal subgroup. This class of groups includes abelain
groups and $p$-groups. Our general result is computationally satisfying when
one can find a suitable representation of $MU^G_*$. For abelian groups the
map to completion at the augmentation ideal seems to be such a
representation, so we make explicit computations of that map. We give
applications to the geometry of lens spaces and $S^1$ actions on stably
complex four-manifolds.
**This paper is a revised version of a previous submission. The biggest
**change is the explicit naming of ring generators of $MU^G_*$.