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arXiv · 2508.05184

Homotopy Invariance of $K$-groups using Grayson's Technique

Sourayan Banerjee
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Abstract

Homotopy invariance of $K$-theory has always been a point of interest. In this article, with the help of the generators of Nil$K$-groups using Grayson's technique, it is shown that if $R$ is a Pr\"{u}fer domain, then $K_n(R) \cong K_n(R[s])$ for all $n>0.$ This is a specific case of the already published work of the author and Vivek Sadhu. However, contrary to the method used before, we specifically prove the isomorphism by showing that Nil$K$-groups vanish.

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Sourayan Banerjee. 2025-08-07. Homotopy Invariance of $K$-groups using Grayson's Technique. https://arxiv.org/abs/2508.05184

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