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2019 Segal operations in the algebraic $K$-theory of topological spaces
Thomas Gunnarsson, Ross Staffeldt
Ann. K-Theory 4(1): 1-56 (2019). DOI: 10.2140/akt.2019.4.1

Abstract

We extend earlier work of Waldhausen which defines operations on the algebraic K -theory of the one-point space. For a connected simplicial abelian group X and symmetric groups Σ n , we define operations θ n : A ( X ) A ( X × B Σ n ) in the algebraic K -theory of spaces. We show that our operations can be given the structure of E -maps. Let ϕ n : A ( X × B Σ n ) A ( X × E Σ n ) A ( X ) be the Σ n -transfer. We also develop an inductive procedure to compute the compositions ϕ n θ n , and outline some applications.

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Thomas Gunnarsson. Ross Staffeldt. "Segal operations in the algebraic $K$-theory of topological spaces." Ann. K-Theory 4 (1) 1 - 56, 2019. https://doi.org/10.2140/akt.2019.4.1

Information

Received: 11 July 2017; Revised: 9 July 2018; Accepted: 31 October 2018; Published: 2019
First available in Project Euclid: 9 April 2019

zbMATH: 07051946
MathSciNet: MR3936014
Digital Object Identifier: 10.2140/akt.2019.4.1

Subjects:
Primary: 19D10
Secondary: 19D23

Keywords: algebraic $K\mkern-2mu$-theory of topological spaces , operations , Segal operations

Rights: Copyright © 2019 Mathematical Sciences Publishers

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