The Gromov width of 4-dimensional tori

Details The Gromov width of 4-dimensional tori The Gromov width of 4-dimensional tori

2011-11-28

arxiv.org/abs/1111.6566v1

Mathematics

Symplectic Geometry

31 pages, 14 figures

Scientific paper

We show that every 4-dimensional torus with a linear symplectic form can be fully filled by one symplectic ball. If such a torus is not symplectomorphic to a product of 2-dimensional tori with equal sized factors, then it can also be fully filled by one symplectic ellipsoid of any shape, or, more generally, by any finite collection of balls or ellipsoids provided only that their total volume is less than that of the 4-torus with its given linear symplectic form.

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