Equivariant orientations and G-bordism theory
type: Item
instance of: scholarly article
title: Equivariant orientations and G-bordism theory
zbMATH Open document ID: 0659.57019
published in: Pacific Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: This paper outlines a new geometric theory of orientations under the action of a group G and formulates bordism theories for G-oriented manifolds. These theories extend the classical G-bordism theories (graded on \({\mathbb{Z}})\), as well as the RO(G)-graded oriented G-bordism theories which describe bordism of G-manifolds with restricted local representation structure. The theories obtained account for oriented and unoriented bordism of G-manifolds with and without restricted local representation structure. It is shown further that there are spectral sequences covering to these theories through adjacent family constructions.
Mathematics Subject Classification ID: 57R85
Mathematics Subject Classification ID: 55N91
Mathematics Subject Classification ID: 57S99
Mathematics Subject Classification ID: 55N22
Mathematics Subject Classification ID: 55T25
zbMATH DE Number: 4078285
zbMATH Keywords: geometric theory of orientations
zbMATH Keywords: action of a group
zbMATH Keywords: bordism theories for G-oriented manifolds
zbMATH Keywords: RO(G)-graded oriented G-bordism theories
zbMATH Keywords: local representation structure
zbMATH Keywords: spectral sequences
author: S. R. Costenoble
author: S. Waner
MaRDI profile type: Publication
full work available at URL: pjm.1989.140.63
OpenAlex ID: W2081688971
DOI: 10.2140/PJM.1989.140.63
description: scientific article; zbMATH DE number 4078285