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Factoring the Becker-Gottlieb Transfer Through the Trace Map

Wojciech Dorabiala·Mark W. Johnson
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Abstract

We verify the Becker-Shultz axioms characterizing the Becker-Gottlieb transfer $τ$ 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), $τ$ 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 $τ$ for arbitrary perfect fibrations, our homotopy equivalence extends to the case of arbitrary perfect fibrations as well.

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Wojciech Dorabiala, Mark W. Johnson. 2009-05-29. Factoring the Becker-Gottlieb Transfer Through the Trace Map. https://arxiv.org/abs/math/0601620

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