### 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 language | English (US) |
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Pages (from-to) | 133-173 |

Number of pages | 41 |

Journal | Pure and Applied Mathematics Quarterly |

Volume | 8 |

Issue number | 1 |

State | Published - Jan 1 2012 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)