English

Shortening binary complexes and commutativity of $K$-theory with infinite products

K-Theory and Homology 2021-05-28 v1

Abstract

We show that in Grayson's model of higher algebraic KK-theory using binary acyclic complexes, the complexes of length two suffice to generate the whole group. Moreover, we prove that the comparison map from Nenashev's model for K1K_1 to Grayson's model for K1K_1 is an isomorphism. It follows that algebraic KK-theory of exact categories commutes with infinite products.

Keywords

Cite

@article{arxiv.1705.09116,
  title  = {Shortening binary complexes and commutativity of $K$-theory with infinite products},
  author = {Daniel Kasprowski and Christoph Winges},
  journal= {arXiv preprint arXiv:1705.09116},
  year   = {2021}
}

Comments

23 pages