English

A remark on the invariance of $K$-theory under duality

K-Theory and Homology 2026-03-10 v1 Algebraic Topology

Abstract

In this short remark, we explain that two examples of invariance under duality for a localizing invariant FF hold purely formally when FF is KK-theory, whereas the general statement for arbitrary localizing invariants does not reduce to a formal statement. We record a counterexample to the claim that the universal localizing invariant is invariant under the operation of taking opposite categories, originally due to Tabuada.

Keywords

Cite

@article{arxiv.2603.08344,
  title  = {A remark on the invariance of $K$-theory under duality},
  author = {Georg Lehner},
  journal= {arXiv preprint arXiv:2603.08344},
  year   = {2026}
}