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Symplectic capacities
from positive $S^1$–equivariant symplectic homology
Jean Gutt and Michael Hutchings |
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Algebraic & Geometric Topology 18 (2018) 3537–3600
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Abstract |
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We use positive –equivariant symplectic homology to define a sequence of symplectic capacities for star-shaped domains in . These capacities are conjecturally equal to the Ekeland–Hofer capacities, but they satisfy axioms which allow them to be computed in many more examples. In particular, we give combinatorial formulas for the capacities of any “convex toric domain” or “concave toric domain”. As an application, we determine optimal symplectic embeddings of a cube into any convex or concave toric domain. We also extend the capacities to functions of Liouville domains which are almost but not quite symplectic capacities. |
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Keywords
symplectic capacities, equivariant symplectic homology,
cube capacity
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Mathematical Subject Classification 2010
Primary: 53D05, 53D40, 57R17
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References |
Publication
Received: 31 October 2017
Revised: 18 May 2018
Accepted: 8 June 2018
Published: 18 October 2018
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Authors |
| Jean Gutt | |
| Mathematical Institute Universität zu Köln Köln Germany |
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| Michael Hutchings | |
| Mathematics Department University of California, Berkeley Berkeley, CA United States |
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