Horizontal decompositions, I

Lisca, Paolo; Parma, Andrea

doi:10.2140/agt.2024.24.3503

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Horizontal decompositions, I

Paolo Lisca and Andrea Parma

Algebraic & Geometric Topology 24 (2024) 3503–3525

DOI: 10.2140/agt.2024.24.3503

Abstract

We show that every smooth closed orientable $4$ –manifold $X$ admits a special kind of handlebody decomposition that we call horizontal. We classify the closed $4$ –manifolds with the simplest horizontal decompositions and we describe all such decompositions of ${ℂ ℙ}^{2}$ , showing that they give rise to infinitely many of the known embeddings of rational homology balls in the complex projective plane.

Keywords

rational homology balls, smooth embeddings, handlebody decompositions

Mathematical Subject Classification

Primary: 57K40

Secondary: 57R40

References

Publication

Received: 18 May 2022

Revised: 21 October 2022

Accepted: 30 October 2022

Published: 7 October 2024

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 24, issue 6 (2024)