A twisted Bass-Heller-Swan decomposition for localising invariants
K-Theory and Homology
2024-10-31 v1 Algebraic Topology
Abstract
We generalise the classical Bass-Heller-Swan decomposition for the K-theory of (twisted) Laurent algebras to a splitting for general localising invariants of certain categories of twisted automorphisms. As an application, we obtain splitting formulas for Waldhausen's A-theory of mapping tori and for the K-theory of certain tensor algebras. We identify the Nil-terms appearing in this splitting in two ways. Firstly, as the reduced K-theory of twisted endomorphisms. Secondly, as the reduced K-theory of twisted nilpotent endomorphisms. Finally, we generalise classical vanishing results for Nil-terms of regular rings to our setting.
Keywords
Cite
@article{arxiv.2410.22877,
title = {A twisted Bass-Heller-Swan decomposition for localising invariants},
author = {Dominik Kirstein and Christian Kremer},
journal= {arXiv preprint arXiv:2410.22877},
year = {2024}
}
Comments
30 pages. Comments welcome!