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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
The Gromov width of $4$–dimensional tori

Janko Latschev, Dusa McDuff and Felix Schlenk

Geometry & Topology 17 (2013) 2813–2853
Abstract

Let ω be any linear symplectic form on the 4–torus T4. We show that in all cases (T4,ω) can be fully filled by one symplectic ball. If (T4,ω) is not symplectomorphic to a product T2(μ) × T2(μ) 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 (T4,ω).

Keywords
Gromov width, symplectic embeddings, symplectic packing, symplectic filling, tori
Mathematical Subject Classification 2010
Primary: 57R17, 57R40
Secondary: 32J27
References
Publication
Received: 27 September 2012
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