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Multiplicative transfers in ordinary cohomology

Published online by Cambridge University Press:  20 January 2009

Richard Steiner
Richard Steiner
Affiliation:
University of GlasgowDepartment of Mathematics, 15 University Gardens, Glasgow G12 8Qw
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In [10] Segal shows that the groups of units in certain ordinary cohomology rings are the zeroth terms of generalised cohomology theories. Geometric methods then give a multiplicative transfer on these groups of units for fibrations with finite fibres; see Kahn and Priddy [6] and Adams ([1], 4). On the other hand Evens [5] by manipulations with cochains has constructed a multiplicative transfer in the cohomology of a group G and a subgroup H of finite index. Now it is well known that the algebraic cohomology of G and H can be identified with the topological cohomology of their classifying spaces BG and BH, and that there is a fibration BH→BG with finite fibres. This suggests that Evens' algebraic transfer and the geometric transfer derived from Segal's work may be related. In the present paper I confirm this by constructing a common generalisation; I also describe some of its properties.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 25 , Issue 2 , June 1982 , pp. 113 - 131
Copyright
Copyright © Edinburgh Mathematical Society 1982

References

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