#### Volume 17, issue 5 (2013)

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The Gromov width of $4$–dimensional tori

### Janko Latschev, Dusa McDuff and Felix Schlenk

Geometry & Topology 17 (2013) 2813–2853
##### Abstract

Let $\omega$ be any linear symplectic form on the $4$–torus ${T}^{4}$. We show that in all cases $\left({T}^{4},\omega \right)$ can be fully filled by one symplectic ball. If $\left({T}^{4},\omega \right)$ is not symplectomorphic to a product ${T}^{2}\left(\mu \right)×{T}^{2}\left(\mu \right)$ of equal sized factors, then it can also be fully filled by any finite collection of balls provided only that their total volume is less than that of $\left({T}^{4},\omega \right)$.

##### Keywords
Gromov width, symplectic embeddings, symplectic packing, symplectic filling, tori
##### Mathematical Subject Classification 2010
Primary: 57R17, 57R40
Secondary: 32J27
##### Publication
Accepted: 13 June 2013
Published: 14 October 2013
Proposed: Leonid Polterovich
Seconded: Danny Calegari, Yasha Eliashberg
##### Authors
 Janko Latschev Fachbereich Mathematik Universität Hamburg Bundesstrasse 55 D-20146 Hamburg Germany Dusa McDuff Mathematics Department Barnard College, Columbia University MC4410 3009 Broadway New York, NY 10027 USA Felix Schlenk Institut de Mathématiques Université de Neuchâtel Rue Emile-Argand 11, CP 158 CH-2000 Neuchâtel Switzerland