Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Transfer and ramified coverings

Larry Smitha1

a1 Mathematisches Institut der Universität, Bunsenstraβe, 3/5, 3400 Göttingen, Bundesrepublik Deutschland

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

S0305004100060795_eqnU1

with the expected property that

S0305004100060795_eqnU2

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 xs211A-acyclic space is again xs211A acyclic.

(Received August 20 1982)

(Revised September 07 1982)