Vol. 112, No. 2, 1984

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Some remarks on the calculation of Stiefel-Whitney classes and a paper of Wu-Yi Hsiang’s

McKenzie Y. K. Wang

Vol. 112 (1984), No. 2, 431–443
Abstract

In this paper we employ the techniques introduced by Wu-Yi Hsiang in [4] to perform Stiefel-Whitney class calculations for the possibilities of connected principal isotropy type listed in Theorems 1–3 of [4]. We show that some of the possibilities listed there do not occur if we assume in addition that sufficiently many Stiefel-Whitney classes of the G-manifold vanish. We therefore obtain a slightly shorter list of possibilities of connected principal isotropy type for compact connected Lie group actions on parallelizable manifolds. Stiefel manifolds which are not spheres, for example, fall under this category. We also give an example of how our results may be used to study actions on Stiefel manifolds. As this paper is actually a supplement to [4], we refer the reader to it for notation and general philosophy.

Mathematical Subject Classification 2000
Primary: 57S15
Milestones
Received: 16 October 1981
Published: 1 June 1984
Authors
McKenzie Y. K. Wang