On transfer maps in the algebraic K-theory of spaces

On transfer maps in the algebraic K-theory of spaces

We show that the Waldhausen trace map Tr X : A ( X ) → Q X + , which defines a natural splitting map from the algebraic K -theory of spaces to stable homotopy, is natural up to weak homotopy with respect to transfer maps in algebraic K -theory and Becker-Gottlieb transfer maps respectively.

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Veröffentlicht in:Mathematische Zeitschrift 2021-02, Vol.297 (1-2), p.729-745
1. Verfasser: Raptis, George
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Mathematics
Mathematics and Statistics
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Zusammenfassung:We show that the Waldhausen trace map Tr X : A ( X ) → Q X + , which defines a natural splitting map from the algebraic K -theory of spaces to stable homotopy, is natural up to weak homotopy with respect to transfer maps in algebraic K -theory and Becker-Gottlieb transfer maps respectively.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-020-02530-8