On transfer maps in the algebraic K-theory of spaces

2019/01/16 by Raptis, George
#Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1901.05539

Abstract

We show that the Waldhausen trace map Tr_X \colon A(X) → QX₊, 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.

Related

• The First Differential of the Functor "Algebraic K-Theory of Spaces"
• Factoring the Becker-Gottlieb Transfer Through the Trace Map
• K-theory of endomorphisms, the TR-trace, and zeta functions
• Algebraic K-theory and trace invariants
• Transfers on Milnor-Witt K-theory