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Unseen symplectic boundaries. (English) Zbl 0870.53020
de Bartolomeis, Paolo (ed.) et al., Manifolds and geometry. Proceedings of a conference, held in Pisa, Italy, September 1993. Cambridge: Cambridge University Press. Symp. Math. 36, 178-189 (1996).
In this paper the authors show that the boundary of a symplectic manifold cannot be completely reconstructed in terms of the interior alone. The main result is as follows: There exist two domains \(\Omega, \Omega'\) with smooth boundaries in the standard symplectic space \(\mathbb{R}^{2n}\), such that their interiors \(\text{Int} \Omega\) and \(\text{Int} \Omega'\) are symplectomorphic but their boundaries \(\partial\Omega\) and \(\partial\Omega'\) are not. The boundaries \(\partial \Omega\) and \(\partial \Omega'\) can be chosen diffeomorphic and, moreover, arbitrarily \(C^\infty\)-close to the round ball \(D^{2n} \subset \mathbb{R}^{2n}\).
For the entire collection see [Zbl 0840.00037].

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
53C40 Global submanifolds