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Packing stability for symplectic $ 4$-manifolds


Authors: O. Buse, R. Hind and E. Opshtein
Journal: Trans. Amer. Math. Soc. 368 (2016), 8209-8222
MSC (2010): Primary 53D05, 57R17
DOI: https://doi.org/10.1090/tran/6802
Published electronically: April 15, 2016
MathSciNet review: 3546797
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Abstract: The packing stability in symplectic geometry was first noticed by Biran (1997): the symplectic obstructions to embed several balls into a manifold disappear when their size is small enough. This phenomenon is known to hold for all closed manifolds with rational symplectic class, as well as for all ellipsoids. In this note, we show that packing stability holds for all closed, and several open, symplectic $ 4$-manifolds.


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Additional Information

O. Buse
Affiliation: Department of Mathematics, Indiana University – Purdue University, Indianapolis, Indiana 46202

R. Hind
Affiliation: Department of Mathematics, University of Notre Dame, 255 Hurley Hall, Notre Dame, Indiana 46556

E. Opshtein
Affiliation: Institut de Recherche Mathematique Avancée UMR 7501, Universite de Strasbourg et CNRS, 7 rue Rene Descartes, 67000 Strasbourg, France

DOI: https://doi.org/10.1090/tran/6802
Received by editor(s): April 28, 2014
Received by editor(s) in revised form: June 23, 2015
Published electronically: April 15, 2016
Additional Notes: The first author was partially supported by NSF grant DMS-1211244
The second author was partially supported by Grant # 317510 from the Simons Foundation
The third author was partially supported by ANR project “hameo” ANR-116JS01-010-01
Article copyright: © Copyright 2016 American Mathematical Society