Horizontal decompositions, II

2023/02/28 by Paolo Lisca, Lisca, Paolo, Andrea Parma +1 · 1 citation
Mathematics · #57K43 #57R17 (Secondary) #57R40 (Primary) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2302.14606

openalex publication_date 2023/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \mathbbCP² and infinitely many more. We also show that a rational ball of our family admits an almost-complex embedding in \mathbbCP² if and only if it admits a symplectic embedding.

Cited by

• The Farey tree and embeddings of lens spaces and rational balls in \mathbbCP²

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• Smooth Embeddings of Rational Homology Balls
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• Smooth, nonsymplectic embeddings of rational balls in the complex projective plane
• Non-smoothable four-manifolds with cyclic fundamental group
• On almost complex embeddings of rational homology balls