Vol. 4, No. 1, 2019

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Segal operations in the algebraic $K\mkern-2mu$-theory of topological spaces

Thomas Gunnarsson and Ross Staffeldt

Vol. 4 (2019), No. 1, 1–56

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 Σn, we define operations θn : A(X) A(X × BΣn) in the algebraic K-theory of spaces. We show that our operations can be given the structure of E-maps. Let ϕn : A(X × BΣn) A(X × EΣn) A(X) be the Σn-transfer. We also develop an inductive procedure to compute the compositions ϕn θn, and outline some applications.

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algebraic $K\mkern-2mu$-theory of topological spaces, Segal operations, operations
Mathematical Subject Classification 2010
Primary: 19D10
Secondary: 19D23
Received: 11 July 2017
Revised: 9 July 2018
Accepted: 31 October 2018
Published: 24 March 2019
Thomas Gunnarsson
Department of Mathematics
Luleå University of Technology
Ross Staffeldt
Department of Mathematical Sciences
New Mexico State University
Las Cruces, NM
United States