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Free S1-actions and involutions on homotopy seven spheres

Published online by Cambridge University Press:  24 October 2008

K. H. Mayer
K. H. Mayer
Affiliation:
University of Dortmund
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Extract

In this note the concept of modest vector bundle, defined in (5), is used to define an invariant for certain free S1-actions. This invariant is a rational function and classifies the equivalence classes of free S1-actions on homotopy seven spheres. In a similar way an invariant for free involutions is defined, which is a generalization of the Spin invariant defined in (4). Using this invariant and Hirzebruch's α-invariant it is possible to state conditions for a free involution of a homotopy seven sphere to be embedded in a free S1-action.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 3 , May 1973 , pp. 455 - 458
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

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