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

Kasprowski, Daniel; Winges, Christoph

doi:10.1090/btran/43

Shortening binary complexes and commutativity of K-theory with infinite products
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by Daniel Kasprowski and Christoph Winges HTML | PDF

Trans. Amer. Math. Soc. Ser. B 7 (2020), 1-23

Abstract:

We show that in Grayson’s model of higher algebraic K-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 $K_1$ to Grayson’s model for $K_1$ is an isomorphism. It follows that algebraic $K$-theory of exact categories commutes with infinite products.

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