Transfer and ramified coverings

Abstract

AbstractIn 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 homomorphismwith the expected property thatis 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.