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arXiv · 1705.09116

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

Daniel Kasprowski·Christoph Winges
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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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Daniel Kasprowski, Christoph Winges. 2017-05-25. Shortening binary complexes and commutativity of $K$-theory with infinite products. https://doi.org/10.1090/btran%2F43

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