Transfers for ramified covering maps in homology and cohomology
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/94651 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |