The $K(π, 1)$ conjecture for affine Artin groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909762739765248 |
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| author | Paolini, Giovanni Salvetti, Mario |
| author_facet | Paolini, Giovanni Salvetti, Mario |
| contents | In this summary paper, we present the key ideas behind the recent proof of the $K(π, 1)$ conjecture for affine Artin groups, which states that complements of locally finite affine hyperplane arrangements with real equations and stable under orthogonal reflections are aspherical. We survey three facets of the argument: the combinatorics of noncrossing partition posets associated with Coxeter groups; the appearance of dual Artin groups and the question of their isomorphism with standard Artin groups; the topological models and their interplay in the proof. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_00445 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $K(π, 1)$ conjecture for affine Artin groups Paolini, Giovanni Salvetti, Mario Group Theory Algebraic Topology Combinatorics Geometric Topology In this summary paper, we present the key ideas behind the recent proof of the $K(π, 1)$ conjecture for affine Artin groups, which states that complements of locally finite affine hyperplane arrangements with real equations and stable under orthogonal reflections are aspherical. We survey three facets of the argument: the combinatorics of noncrossing partition posets associated with Coxeter groups; the appearance of dual Artin groups and the question of their isomorphism with standard Artin groups; the topological models and their interplay in the proof. |
| title | The $K(π, 1)$ conjecture for affine Artin groups |
| topic | Group Theory Algebraic Topology Combinatorics Geometric Topology |
| url | https://arxiv.org/abs/2509.00445 |