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

Richter, Birgit

doi:10.2140/agt.2010.10.315

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

Birgit Richter

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 $K (k u)$ , $K (k o)$ and Waldhausen’s $A$ –theory of spaces of the form $B B G$ , 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 2000

Primary: 55S25, 19D23

Secondary: 19D10

References

Publication

Received: 29 September 2008

Revised: 22 June 2009

Accepted: 23 June 2009

Published: 19 February 2010

Authors

Birgit Richter
Department Mathematik der Universität Hamburg Bundesstraße 55 20146 Hamburg Germany
http://www.math.uni-hamburg.de/home/richter/

Volume 10, issue 1 (2010)