Horizontal decompositions, II

Lisca, Paolo; Parma, Andrea

doi:10.2140/agt.2025.25.2179

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Horizontal decompositions, II

Paolo Lisca and Andrea Parma

Algebraic & Geometric Topology 25 (2025) 2179–2207

DOI: 10.2140/agt.2025.25.2179

Abstract

We complete the classification of the smooth, closed, oriented $4$ -manifolds having Euler characteristic less than four and a horizontal handlebody decomposition of genus one. We use the classification result to find a large family of rational homology ball smoothings of cyclic quotient singularities which can be smoothly embedded into the complex projective plane. Our family contains all such rational balls previously known to embed into ${ℂ ℙ}^{2}$ and infinitely many more. We also show that a rational ball of our family admits an almost-complex embedding in ${ℂ ℙ}^{2}$ if and only if it admits a symplectic embedding.

Keywords

rational homology balls, smooth embeddings, handlebody decompositions

Mathematical Subject Classification

Primary: 57K40

Secondary: 57K43, 57R17

References

Publication

Received: 12 March 2023

Revised: 9 March 2024

Accepted: 7 April 2024

Published: 11 August 2025

Authors

Paolo Lisca
Department of Mathematics University of Pisa Pisa Italy

Andrea Parma
Department of Mathematics University of Pisa Pisa Italy

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Volume 25, issue 4 (2025)