Vol. 77, No. 2, 1978

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ISSN: 0030-8730
Smooth G-manifolds as collections of fiber bundles

Michael Walter Davis

Vol. 77 (1978), No. 2, 315–363
Abstract

This paper is about the general theory of differentiable actions of compact Lie groups. Let G be a compact Lie group acting smoothly on a manifold M. Both M and M∕G have natural stratifications, and M∕G inherits a “smooth structure” from M. The map M M∕G exhibits many of the properties of a smooth fiber bundle. For example, it is proved that a smooth G-manifold can be pulled back via a “weakly stratified” map of orbit spaces. Also, it is well-known (and obvious) that a smooth G-manifold is determined by a certain collection of fiber bundles together with some attaching data. Several precise formulations of this observation are given.

Mathematical Subject Classification 2000
Primary: 57S15
Milestones
Received: 6 October 1976
Published: 1 August 1978
Authors
Michael Walter Davis
Department of Mathematics
The Ohio State University
Columbus OH 43210
United States