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A concave holomorphic filling of an overtwisted contact $3$–sphere

Naohiko Kasuya and Daniele Zuddas

Algebraic & Geometric Topology 23 (2023) 2141–2156
Abstract

We prove that the closed 4–ball admits non-Kähler complex structures with strongly pseudoconcave boundary. Moreover, the induced contact structure on the boundary 3–sphere is overtwisted.

Keywords
non-Kähler complex surface, overtwisted contact 3–manifold, concave filling
Mathematical Subject Classification
Primary: 32V40
Secondary: 32Q55, 57R17
References
Publication
Received: 4 October 2020
Revised: 14 October 2021
Accepted: 16 December 2021
Published: 25 July 2023
Authors
Naohiko Kasuya
Department of Mathematics
Hokkaido University
Sapporo
Japan
Daniele Zuddas
Dipartimento di Matematica e Geoscienze
University of Trieste
Trieste
Italy
https://www.danielezuddas.eu

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