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Segal operations in the algebraic K-theory of topological spaces
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Department of Mathematical Sciences New Mexico State University Las Cruces, NM United States.
2019 (engelsk)Inngår i: Annals of K-Theory, ISSN 2379-1683, Vol. 4, nr 1, s. 1-56Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
Mathematical science publ , 2019. Vol. 4, nr 1, s. 1-56
Emneord [en]
algebraic K-theory of topological spaces, Segal operations, operations
HSV kategori
Forskningsprogram
Matematik
Identifikatorer
URN: urn:nbn:se:ltu:diva-73694DOI: 10.2140/akt.2019.4.1ISI: 000463773200001OAI: oai:DiVA.org:ltu-73694DiVA, id: diva2:1305585
Merknad

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

Tilgjengelig fra: 2019-04-17 Laget: 2019-04-17 Sist oppdatert: 2019-08-20bibliografisk kontrollert

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