Forbidden configurations and definite fillings of lens spaces
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918292042547200 |
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| author | Fung, Antony T. H. Park, JungHwan |
| author_facet | Fung, Antony T. H. Park, JungHwan |
| contents | We study definite fillings of lens spaces. We classify the lens spaces $L(p,q)$ for which every smooth negative-definite filling $X$ satisfies \[ b_2(X)\ge b_2(X(p,q))-1, \] where $X(p,q)$ denotes the canonical negative-definite plumbing. The classification is given by 17 "forbidden configurations" that cannot appear as induced subgraphs of the canonical plumbing graph. More generally, we introduce a combinatorial framework that encodes the lattice embedding information coming from the dual plumbing of $X(p,q)$, and we prove that it is governed by a finite set of minimal forbidden configurations. We also discuss consequences for symplectic fillings of lens spaces and for smoothings of cyclic quotient singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11083 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Forbidden configurations and definite fillings of lens spaces Fung, Antony T. H. Park, JungHwan Geometric Topology 57K41, 57K43, 57-08 We study definite fillings of lens spaces. We classify the lens spaces $L(p,q)$ for which every smooth negative-definite filling $X$ satisfies \[ b_2(X)\ge b_2(X(p,q))-1, \] where $X(p,q)$ denotes the canonical negative-definite plumbing. The classification is given by 17 "forbidden configurations" that cannot appear as induced subgraphs of the canonical plumbing graph. More generally, we introduce a combinatorial framework that encodes the lattice embedding information coming from the dual plumbing of $X(p,q)$, and we prove that it is governed by a finite set of minimal forbidden configurations. We also discuss consequences for symplectic fillings of lens spaces and for smoothings of cyclic quotient singularities. |
| title | Forbidden configurations and definite fillings of lens spaces |
| topic | Geometric Topology 57K41, 57K43, 57-08 |
| url | https://arxiv.org/abs/2601.11083 |