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arXiv · 0804.0401

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

Birgit Richter
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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 algebraic K-theory of connective complex and real topological K-theory and Waldhausen's K-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.

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Birgit Richter. 2008-09-29. An involution on the K-theory of bimonoidal categories with anti-involution. https://doi.org/10.2140/agt.2010.10.315

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