Factoring the Becker-Gottlieb transfer through the trace map

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Abstract

In 1998, Becker and Schultz [6] published axioms characterizing the Becker-Gottlieb transfer τBG (p):E(B+) → E (E+) for certain types of fibrations p: E → B. We verify these axioms for the composite of the algebraic K-theory transfer τK (p) E (B+) → A(E) of any perfect fibration p followed by the evaluation (at the unit) from the free loop space Λ of the Bökstedt trace map tr: A(E) → E (ΛE+) → E (E+). As a consequence, for p any compact ANR fibration with finite CW base (those considered by Becker-Shultz), τBG (p) tr τK (p).

Original languageEnglish (US)
Pages (from-to)133-173
Number of pages41
JournalPure and Applied Mathematics Quarterly
Volume8
Issue number1
DOIs
StatePublished - Jan 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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