Factoring the Becker-Gottlieb Transfer Through the Trace Map

Details Factoring the Becker-Gottlieb Transfer Through the Trace Map Factoring the Becker-Gottlieb Transfer Through the Trace Map

2006-01-25

arxiv.org/abs/math/0601620v3

Mathematics

K-Theory and Homology

v3: 29 pages. Revised per referee's suggestions, to appear

Scientific paper

We verify the Becker-Shultz axioms characterizing the Becker-Gottlieb transfer $\tau$ for the composite of the algebraic K-theory transfer of any perfect fibration followed by the trace map. As a consequence, for any compact ANR fibration (those considered by Becker-Shultz), $\tau$ is homotopy equivalent to the composite of the algebraic K-theory transfer followed by the trace map. Furthermore, if these same axioms (including strong additivity) could be shown to extend to characterizing $\tau$ for arbitrary perfect fibrations, our homotopy equivalence extends to the case of arbitrary perfect fibrations as well.

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