刺穿仿射空间中自同态的朴素同伦类上的单群结构

IF 0.5 4区数学 Q2 MATHEMATICS

Journal of Homotopy and Related Structures Pub Date : 2025-06-16 DOI:10.1007/s40062-025-00373-w

Thomas Brazelton, William Hornslien

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引用次数: 0

摘要

Cazanave证明了射影线自同态的朴素\(\mathbb {A}^1\) -同伦类集合允许一个群补全为射影线自同态的真\(\mathbb {A}^1\) -同伦类的单似结构。在这篇简短的笔记中，我们证明，在一个非二次封闭的域上，对于\(n\ge 2\)的刺穿仿射空间\(\mathbb {A}^n\hspace{-0.1em}\smallsetminus \{0\}\)，这样的陈述永远不成立。

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Concerning monoid structures on naive homotopy classes of endomorphisms of punctured affine space

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, over a field which is not quadratically closed, such a statement is never true for punctured affine space \(\mathbb {A}^n\hspace{-0.1em}\smallsetminus \{0\}\) for \(n\ge 2\).

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来源期刊

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.