Algebraic & Geometric Topology 10 (2010) 315–342

DOI: 10.2140/agt.2010.10.315

Abstract

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.

Keywords

algebraic K–theory, topological K–theory, involution, Waldhausen A–theory

Mathematical Subject Classification

Primary: 19D23, 55S25

Secondary: 19D10

References

Publication

Received: 29 September 2008
Revised: 22 June 2009
Accepted: 23 June 2009
Published: 19 February 2010

Authors