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arXiv · 2506.09905

Combinatorial relative algebraic $K$-theory

Jane Turner
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Abstract

In a preprint released in 2016, Daniel Grayson introduces a conjectural presentation of the (higher) relative algebraic $K$-groups using purely combinatorial means. In this paper, we will show that this presentation is isomorphic to the classically defined higher relative algebraic $K$-groups, and provide some reasons to believe the conjecture posed in this 2016 preprint to be true.

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Jane Turner. 2025-06-11. Combinatorial relative algebraic $K$-theory. https://arxiv.org/abs/2506.09905

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