Unoriented Bordism and Actions of Finite Groups
R. E. Stong
§ 1. Introduction
The object of this paper is an analysis of the equivariant
homology theories arising from equivariant unoriented bordism.
In their monumental work
P. E. Conner and E. E. Floyd demonstrated the effectiveness of
bordism methods in the analysis of group actions. In a later
work, "Maps of odd period", Conner and Floyd established a
framework for the study of actions of an arbitrary finite group
G on compact manifolds. The author [9,10] has indicated that
their methods may be applied to equivariant bordism as well.
The program attempted here may be described roughly as:
1) Define equivariant bordism groups by taking equivalence
classes of equivariant maps of compact G manifolds into G spaces.
2) Analyze the bordism groups by means of the fixed point
structure, reducing their calculation to "simpler" equivariant
3) Solve the resulting "simpler" problem.
In most of the cases considered by Conner and Floyd the "simpler"
problem is an ordinary bordism problem. For more general groups
one obtains other equivariant problems, but may iterate the process.
The structure theorems obtained are related to results of
Received by the editors May 8, 1970