The symplectic topology of Ramanujam's surface
| dc.creator | Seidel, Paul | |
| dc.creator | Smith, Ivan | |
| dc.date | 2004-11-26 | |
| dc.date | 2005-06-28 | |
| dc.date.accessioned | 2026-07-07T05:14:44Z | |
| dc.date.available | 2026-07-07T05:14:44Z | |
| dc.description | Ramanujam's surface M is a contractible affine algebraic surface which is not homeomorphic to the affine plane. For any m>1 the product M^m is diffeomorphic to Euclidean space R^{4m}. We show that, for every m>0, M^m cannot be symplectically embedded into a subcritical Stein manifold. This gives the first examples of exotic symplectic structures on Euclidean space which are convex at infinity. It follows that any exhausting plurisubharmonic Morse function on M^m has at least three critical points, answering a question of Eliashberg. The heart of the argument involves showing a particular Lagrangian torus L inside M cannot be displaced from itself by any Hamiltonian isotopy, via a careful study of pseudoholomorphic discs with boundary on L. | |
| dc.description | 22 pages, 2 figures. Version 2 has referee's clarifications, this version to appear in Comment. Math. Helv | |
| dc.identifier | https://arxiv.org/abs/math/0411601 | |
| dc.identifier | http://arxiv.org/abs/math/0411601 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73393 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 53D35; 14R10 | |
| dc.title | The symplectic topology of Ramanujam's surface | |
| dc.type | text |