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Segal operations in the algebraic K-theory of topological spaces
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Department of Mathematical Sciences New Mexico State University Las Cruces, NM United States.
2019 (English)In: Annals of K-Theory, ISSN 2379-1683, Vol. 4, no 1, p. 1-56Article in journal (Refereed) Published
Abstract [en]

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 Sigma(n) we define operations theta(n) : A(X) -> A(X x B Sigma(n)) in the algebraic K-theory of spaces. We show that our operations can be given the structure of E-infinity-maps. Let phi(n) : A(X x B Sigma(n)) -> A(X x E Sigma(n)) similar or equal to A(X) be the Sigma(n)-transfer. We also develop an inductive procedure to compute the compositions phi(n) circle theta(n) and outline some applications.

Place, publisher, year, edition, pages
Mathematical science publ , 2019. Vol. 4, no 1, p. 1-56
Keywords [en]
algebraic K-theory of topological spaces, Segal operations, operations
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-73694DOI: 10.2140/akt.2019.4.1ISI: 000463773200001OAI: oai:DiVA.org:ltu-73694DiVA, id: diva2:1305585
Note

Validerad;2019;Nivå 2;2019-08-20 (johcin)

Available from: 2019-04-17 Created: 2019-04-17 Last updated: 2019-08-20Bibliographically approved

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Gunnarsson, Thomas

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