The Gromov width of 4–dimensional tori

Latschev, Janko¹ ; McDuff, Dusa² ; Schlenk, Felix³

¹ Fachbereich Mathematik, Universität Hamburg, Bundesstrasse 55, D-20146 Hamburg, Germany
² Mathematics Department, Barnard College, Columbia University, MC4410, 3009 Broadway, New York, NY 10027, USA
³ Institut de Mathématiques, Université de Neuchâtel, Rue Emile-Argand 11, CP 158, CH-2000 Neuchâtel, Switzerland

Geometry & topology, Tome 17 (2013) no. 5, pp. 2813-2853.

Résumé

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 $T^2\left(\mu \right)\times T^2\left(\mu \right)$ 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 $\left(T^4,\omega \right)$.

Détail

DOI : 10.2140/gt.2013.17.2813

Classification : 57R17, 57R40, 32J27
Keywords: Gromov width, symplectic embeddings, symplectic packing, symplectic filling, tori

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