Transfer and ramified coverings

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 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.