#### Vol. 10, No. 8, 2017

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Complete embedded complex curves in the ball of $\mathbb{C}^2$ can have any topology

### Antonio Alarcón and Josip Globevnik

Vol. 10 (2017), No. 8, 1987–1999
##### Abstract

In this paper we prove that the unit ball $\mathbb{B}$ of ${ℂ}^{2}$ admits complete properly embedded complex curves of any given topological type. Moreover, we provide examples containing any given closed discrete subset of $\mathbb{B}$.

##### Keywords
complex curves, holomorphic embeddings, complete bounded submanifolds
##### Mathematical Subject Classification 2010
Primary: 32H02, 32B15, 32C22
##### Milestones
Accepted: 29 June 2017
Published: 18 August 2017
##### Authors
 Antonio Alarcón Departamento de Geometría y Topología e Instituto de Matemáticas (IEMath-GR) Universidad de Granada Granada Spain Josip Globevnik Department of Mathematics and Institute of Mathematics, Physics and Mechanics University of Ljubljana Ljubljana Slovenia