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Differentiable Montgomery-Samelson Fiberings with Finite Singular Sets

Published online by Cambridge University Press:  20 November 2018

Peter L. Antonelli
Peter L. Antonelli*
Affiliation:
The University of Tennessee, Knoxville, Tennessee
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In 1946 Montgomery and Samelson (11) introduced a generalization of the notion of a differentiable group action with one type of orbit besides fixed points. Such an object is essentially a locally trivial fibering except on a certain singular set over which fibres are pinched to points. In recent years there has been a fair amount of research on these MS-fiberings and similar singular fiberings. This paper is another effort in this direction. For a fairly complete bibliography of the literature, the reader should consult the references, and in particular, (5).

Let f: Mn → Sp, with Mn a closed connected n-manifold and Sp the unit p-sphere with standard differentiable structure, be the projection map of a smooth MS-fibering with finite non-empty singular set.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 1489 - 1495
Copyright
Copyright © Canadian Mathematical Society 1969

References

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