Coisotropic displacement and small subsets of a symplectic manifold

We prove a coisotropic intersection result and deduce the following: (a) Lower bounds on the displacement energy of a subset of a symplectic manifold, in particular a sharp stable energy-Gromov-width inequality. (b) A stable non-squeezing result for neighborhoods of products of unit spheres. (c) Exi...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2012-06, Vol.271 (1-2), p.415-445
Main Authors: Swoboda, Jan, Ziltener, Fabian
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We prove a coisotropic intersection result and deduce the following: (a) Lower bounds on the displacement energy of a subset of a symplectic manifold, in particular a sharp stable energy-Gromov-width inequality. (b) A stable non-squeezing result for neighborhoods of products of unit spheres. (c) Existence of a “badly squeezable” set in of Hausdorff dimension at most d , for every n  ≥ 2 and d  ≥ n . (d) Existence of a stably exotic symplectic form on , for every n  ≥ 2. (e) Non-triviality of a new capacity, which is based on the minimal action of a regular coisotropic submanifold of dimension d .
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-011-0870-2