On lens spaces bounding smooth 4-manifolds with $\boldsymbol{b_2=1}$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916477980901376 |
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| author | Jo, Woohyeok Park, Jongil Park, Kyungbae |
| author_facet | Jo, Woohyeok Park, Jongil Park, Kyungbae |
| contents | We study which lens spaces can bound smooth 4-manifolds with second Betti number one under various topological conditions. Specifically, we show that there are infinite families of lens spaces that bound compact, simply-connected, smooth 4-manifolds with second Betti number one, yet cannot bound a 4-manifold consisting of a single 0-handle and 2-handle. Additionally, we establish the existence of infinite families of lens spaces that bound compact, smooth 4-manifolds with first Betti number zero and second Betti number one, but cannot bound simply-connected 4-manifolds with second Betti number one. The construction of such 4-manifolds with lens space boundaries is motivated by the study of rational homology projective planes with cyclic quotient singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22719 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On lens spaces bounding smooth 4-manifolds with $\boldsymbol{b_2=1}$ Jo, Woohyeok Park, Jongil Park, Kyungbae Geometric Topology Algebraic Geometry 57K30, 57K41, 14J17 We study which lens spaces can bound smooth 4-manifolds with second Betti number one under various topological conditions. Specifically, we show that there are infinite families of lens spaces that bound compact, simply-connected, smooth 4-manifolds with second Betti number one, yet cannot bound a 4-manifold consisting of a single 0-handle and 2-handle. Additionally, we establish the existence of infinite families of lens spaces that bound compact, smooth 4-manifolds with first Betti number zero and second Betti number one, but cannot bound simply-connected 4-manifolds with second Betti number one. The construction of such 4-manifolds with lens space boundaries is motivated by the study of rational homology projective planes with cyclic quotient singularities. |
| title | On lens spaces bounding smooth 4-manifolds with $\boldsymbol{b_2=1}$ |
| topic | Geometric Topology Algebraic Geometry 57K30, 57K41, 14J17 |
| url | https://arxiv.org/abs/2410.22719 |