The Gromov width of 4–dimensional tori

Latschev, Janko; McDuff, Dusa; Schlenk, Felix

doi:10.2140/gt.2013.17.2813

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The Gromov width of $4$–dimensional tori

Janko Latschev, Dusa McDuff and Felix Schlenk

Geometry & Topology 17 (2013) 2813–2853

DOI: 10.2140/gt.2013.17.2813

Abstract

Let $ω$ be any linear symplectic form on the $4$ –torus $T^{4}$ . We show that in all cases $(T^{4}, ω)$ can be fully filled by one symplectic ball. If $(T^{4}, ω)$ is not symplectomorphic to a product $T^{2} (μ) \times T^{2} (μ)$ 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 $(T^{4}, ω)$ .

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

Volume 17, issue 5 (2013)