Transfers for ramified coverings in homology and cohomology

Primary 55R12, 57M12; Secondary 55Q05, 55R35, 57M10

Transfer, ramified covering maps, classifying spaces 

Marcelo A. Aguilar and  Carlos Prieto

Abstract

Making use of a modified version, due to McCord, of the Dold-Thom construction of ordinary homology, we give a simple topological definition of a transfer for ramified covering maps in homology with arbitrary coefficients. The transfer is induced by a suitable map between topological groups. We also define a cohomology transfer which is dual to the homology transfer. This duality allows us to show that our homology transfer coincides with the one given by L. Smith. With our definition of the homology transfer we can give simpler proofs of the properties of the known transfer and of some new ones.