The symplectic topology of Ramanujam's surface

Details The symplectic topology of Ramanujam's surface The symplectic topology of Ramanujam's surface

2004-11-26

arxiv.org/abs/math/0411601v2

Mathematics

Symplectic Geometry

22 pages, 2 figures. Version 2 has referee's clarifications, this version to appear in Comment. Math. Helv

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The symplectic topology of Ramanujam's surface does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The symplectic topology of Ramanujam's surface, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The symplectic topology of Ramanujam's surface will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-353459