Summary
An example of a 4-dimensional symplectic manifold with disconnected boundary of contact type is constructed. A collection of other results about symplectic manifolds with contact-type boundaries are derived using the theory ofJ-holomorphic spheres. In particular, the following theorem of Eliashberg-Floer-McDuff is proved: if a neighbourhood of the boundary of (V, ω) is symplectomorphic to a neighbourhood ofS 2n−1 in standard Euclidean space, and if ω vanishes on all 2-spheres inV, thenV is diffeomorphic to the ballB 2n.
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Oblatum 19-III-1990
Partially supported by NSF grant no: DMS 8803056
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McDuff, D. Symplectic manifolds with contact type boundaries. Invent Math 103, 651–671 (1991). https://doi.org/10.1007/BF01239530
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DOI: https://doi.org/10.1007/BF01239530