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Some unexpectedly non-singular orbit spaces
Published online by Cambridge University Press: 24 October 2008
Extract
The orbit space of a manifold under the smooth action of a compact Lie group is typically a ‘manifold with singularities’. The orbits of a given type each form a mani-fold, but these ‘strata’ generally do not give a manifold when pieced together. For example, the orbit space of S3 under the action of given by the matrix.
is the suspension of P(2), which fails to be a manifold at the suspension points.
In this paper I shall give examples where, in spite of having many orbit types, the orbit space is a manifold, with or without boundary.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 82 , Issue 1 , July 1977 , pp. 35 - 37
- Copyright
- Copyright © Cambridge Philosophical Society 1977