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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 93, Issue 3
  • May 1983, pp. 485-493

Transfer and ramified coverings

  • Larry Smith (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100060795
  • Published online: 24 October 2008
Abstract
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 YY/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.

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(2)A. Dold and R. Thom Quasifaserungen und vinendliche symnaetrische Produkte. Ann. of Math. 67 (1958), 239281.

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  • ISSN: 0305-0041
  • EISSN: 1469-8064
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