There is no Cazanave's Theorem for punctured affine space
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913529386237952 |
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| author | Brazelton, Thomas Hornslien, William |
| author_facet | Brazelton, Thomas Hornslien, William |
| contents | 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 $n \ge 2$ . |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02668 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | There is no Cazanave's Theorem for punctured affine space Brazelton, Thomas Hornslien, William Algebraic Topology Algebraic Geometry 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 $n \ge 2$ . |
| title | There is no Cazanave's Theorem for punctured affine space |
| topic | Algebraic Topology Algebraic Geometry |
| url | https://arxiv.org/abs/2410.02668 |