English

A Fundamental Theorem for the $K$-theory of connective $\mathbb{S}$-algebras

K-Theory and Homology 2020-04-21 v4 Algebraic Topology

Abstract

Invoking the density argument of Dundas-Goodwillie-McCarthy, we extend the Fundamental Theorem of KK-theory from the category of simplicial rings to the category of S\mathbb{S}-algebras. As an intermediate step, we prove the Fundamental Theorem for simplicial rings appealing to recent results from the first author's thesis. This recovers as a special case the Fundamental Theorem for the KK-theory of spaces appearing in H\"uttemann-Klein-Vogell-Waldhausen-Williams.

Keywords

Cite

@article{arxiv.1804.00975,
  title  = {A Fundamental Theorem for the $K$-theory of connective $\mathbb{S}$-algebras},
  author = {Ernest E. Fontes and Crichton Ogle},
  journal= {arXiv preprint arXiv:1804.00975},
  year   = {2020}
}

Comments

Revised and slightly restructured. 18 pages