Horizontal decompositions, II

Lisca, Paolo¹ ; Parma, Andrea¹

¹Department of Mathematics, University of Pisa, Pisa, Italy

Algebraic and Geometric Topology, Tome 25 (2025) no. 4, pp. 2179-2207

Résumé

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 ℂℙ2 and infinitely many more. We also show that a rational ball of our family admits an almost-complex embedding in ℂℙ2 if and only if it admits a symplectic embedding.

Détail

DOI : 10.2140/agt.2025.25.2179

Keywords: rational homology balls, smooth embeddings, handlebody decompositions

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