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On lens spaces bounding
smooth $4$-manifolds with $b_2=1$
Woohyeok Jo, Jongil Park and Kyungbae Park |
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Algebraic & Geometric Topology 26 (2026) 2659–2688
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Abstract |
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We study which lens spaces can bound smooth -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 -manifolds with second Betti number one, yet cannot bound a -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 -manifolds with first Betti number zero and second Betti number one, but cannot bound simply connected -manifolds with second Betti number one. The construction of such -manifolds with lens space boundaries is motivated by the study of rational homology projective planes with cyclic quotient singularities. |
Keywords
lens spaces, Donaldson's diagonalization theorem, rational
homology projective planes
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Mathematical Subject Classification
Primary: 14J17, 57K30, 57K41
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References |
Publication
Received: 16 February 2025
Revised: 9 September 2025
Accepted: 9 October 2025
Published: 1 September 2026
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Authors |
| Woohyeok Jo | |
| Department of Mathematical
Sciences Seoul National University Seoul South Korea |
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| Jongil Park | |
| Department of Mathematical
Sciences Seoul National University Seoul South Korea |
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| Kyungbae Park | |
| Department of Mathematics Kangwon National University Gangwon South Korea |
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| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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