On symplectic fillings of small Seifert 3–manifolds

Choi, Hakho; Park, Jongil

doi:10.2140/agt.2023.23.3497

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On symplectic fillings of small Seifert $3$–manifolds

Hakho Choi and Jongil Park

Algebraic & Geometric Topology 23 (2023) 3497–3530

DOI: 10.2140/agt.2023.23.3497

Abstract

We investigate the minimal symplectic fillings of small Seifert $3$ –manifolds with a canonical contact structure. As a result, we list all minimal symplectic fillings using curve configurations for small Seifert $3$ –manifolds satisfying certain conditions. Furthermore, we also demonstrate that every such a minimal symplectic filling is obtained by a sequence of rational blowdowns from the minimal resolution of the corresponding weighted homogeneous complex surface singularity.

Keywords

rational blowdown, small Seifert 3–manifold, symplectic filling

Mathematical Subject Classification

Primary: 53D05, 57R17

Secondary: 32S25

References

Publication

Received: 26 August 2020

Revised: 12 July 2022

Accepted: 26 July 2022

Published: 5 November 2023

Authors

Hakho Choi
School of Mathematics Korea Institute for Advanced Study Seoul South Korea

Jongil Park
Department of Mathematical Sciences Seoul National University Seoul South Korea

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Volume 23, issue 8 (2023)