Group actions on quasi-symplectic manifolds
type: Item
instance of: scholarly article
title: Group actions on quasi-symplectic manifolds
zbMATH Open document ID: 0726.57030
DOI: 10.1007/BF01445202
published in: Mathematische Annalen
publication date: 1992-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164861
review text: Let M be a quasi-symplectic manifold, this means that M is a closed differentiable manifold such that the tangent bundle of M is a direct sum of quaternionic tensor products. Assume that M admits a non-trivial differentiable action of the circle group which preserves the quasi- symplectic structure. In this case it is possible to compute the rotation numbers of the normal bundle of each connected component of the fixed point set from the rotation numbers of the quaternionic bundles given by the quasi-symplectic structure of M. This is used to deduce vanishing theorems for a set of characteristic numbers of M from a result which was proved in a joint paper with \textit{R. L. E. Schwarzenberger} [Proc. Camb. Philos. Soc. 73, 439-453 (1973; Zbl 0258.58013)]. These theorems are applied to compute the Pontryagin classes of cohomology quaternionic projective spaces which are quasi-symplectic and admit a differentiable non-trivial structure preserving action of the circle group.
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 4199064
zbMATH Keywords: quasi-symplectic manifold
zbMATH Keywords: tangent bundle
zbMATH Keywords: differentiable action
zbMATH Keywords: circle group
zbMATH Keywords: characteristic numbers
zbMATH Keywords: Pontryagin classes
author: K. H. Mayer
reviewed by: K. H. Mayer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4199064