An involution on the K–theory of bimonoidal categories with anti-involution

Richter, Birgit¹

¹Department Mathematik der Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany

Algebraic and Geometric Topology, Tome 10 (2010) no. 1, pp. 315-342

Résumé

We construct a combinatorially defined involution on the algebraic K–theory of the ring spectrum associated to a bimonoidal category with anti-involution. Particular examples of such are braided bimonoidal categories. We investigate examples such as K(ku), K(ko) and Waldhausen’s A–theory of spaces of the form BBG, for abelian groups G. We show that the involution agrees with the classical one for a bimonoidal category associated to a ring and prove that it is not trivial in the above mentioned examples.

Détail

DOI : 10.2140/agt.2010.10.315

Keywords: algebraic $K$–theory, topological $K$–theory, involution, Waldhausen $A$–theory

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