Vol. 77, No. 2, 1978

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Smooth G-manifolds as collections of fiber bundles

Michael Walter Davis

Vol. 77 (1978), No. 2, 315–363

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
Received: 6 October 1976
Published: 1 August 1978
Michael Walter Davis
Department of Mathematics
The Ohio State University
Columbus OH 43210
United States