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arXiv · 2410.02668

There is no Cazanave's Theorem for punctured affine space

Thomas Brazelton·William Hornslien
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Abstract

In his thesis, Cazanave proved that the set of naive $\mathbb{A}^1$-homotopy classes of endomorphisms of the projective line admits a monoid structure whose group completion is genuine $\mathbb{A}^1$-homotopy classes of endomorphisms of the projective line. In this very short note we show that such a statement is never true for punctured affine space $\mathbb{A}^n\setminus\{0\}$ for $n \ge 2$ .

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BibTeXRIS

Thomas Brazelton, William Hornslien. 2024-10-03. There is no Cazanave's Theorem for punctured affine space. https://arxiv.org/abs/2410.02668

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