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Some unexpectedly non-singular orbit spaces

Published online by Cambridge University Press:  24 October 2008

H. R. Morton
H. R. Morton
Affiliation:
University of Liverpool
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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

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References

REFERENCES

(1)Hsiang, W.-C. and Hsiang, W.-Y.Differentiable actions of compact classical groups. I. Amer. J. Math. 89 (1967), 705–786.CrossRefGoogle Scholar
(2)Spanier, E. H.Algebraic Topology (McGraw-Hill, 1966).Google Scholar