Equivariant orientations and G-bordism theory

Steven R. Costenoble and Stefan Waner

Vol. 140 (1989), No. 1, 63–84

DOI: 10.2140/pjm.1989.140.63

Abstract

We outline a new geometric theory of orientations under the action of a group G and formulate bordism theories for G-oriented manifolds. These theories extend the classical G-bordism theories (graded on ℤ), as well as the RO(G)-graded oriented G-bordism theories which describe bordism of G-manifolds with restricted local representation structure. The theories we obtain account for oriented and unoriented bordism of G-manifolds with and without restricted local representation structure. We further obtain spectral sequences converging to these theories through adjacent family constructions.

Mathematical Subject Classification 2000

Primary: 57R85

Milestones

Received: 30 October 1987

Revised: 8 February 1989

Published: 1 November 1989