English

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

Algebraic Topology 2014-10-01 v3 K-Theory and Homology

Abstract

We construct a combinatorially defined involution on the algebraic KK-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.

Keywords

Cite

@article{arxiv.0804.0401,
  title  = {An involution on the K-theory of bimonoidal categories with anti-involution},
  author = {Birgit Richter},
  journal= {arXiv preprint arXiv:0804.0401},
  year   = {2014}
}
R2 v1 2026-06-21T10:27:05.014Z