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Transfer and ramified coverings

Published online by Cambridge University Press:  24 October 2008

Larry Smith
Larry Smith
Affiliation:
Mathematisches Institut der Universität, Bunsenstraβe, 3/5, 3400 Göttingen, Bundesrepublik Deutschland
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Abstract

In this note we introduce a general class of finite ramified coverings π X˜ ↓ X. Examples of ramified covers in our sense include: finite covering spaces, branched covering spaces and the orbit map Y ↓ Y/G where G is a finite group and Y an arbitrary G-space. For any d-fold ramified covering π: X˜ ↓ X we construct a transfer homomorphism

with the expected property that

is multiplication by d. As a consequence we obtain a simple proof of the Conner conjecture; viz. the orbit space of an arbitrary finite group action on a ℚ-acyclic space is again ℚ acyclic.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 3 , May 1983 , pp. 485 - 493
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

REFERENCES

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