International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 94651, 28 pages

Transfers for ramified covering maps in homology and cohomology

Marcelo A. Aguilar and Carlos Prieto

Instituto de Matemáticas, Universidad Nacional Autónoma de México (UNAM), México 04510, DF, Mexico

Received 18 May 2005; Accepted 5 March 2006

Copyright © 2006 Marcelo A. Aguilar and Carlos Prieto. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 new 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. Our transfers can also be defined in Karoubi's approach to homology and cohomology. Furthermore, we show that one can define mixed transfers from other homology or cohomology theories to the ordinary ones.