Lefschetz fibrations and exotic symplectic structures on cotangent bundles of spheres

Details Lefschetz fibrations and exotic symplectic structures on cotangent bundles of spheres Lefschetz fibrations and exotic symplectic structures on cotangent bundles of spheres

2009-06-11

arxiv.org/abs/0906.2230v2

Mathematics

Symplectic Geometry

26 pages, 10 figures; v2 with modified exposition

Scientific paper

We construct open symplectic manifolds which are convex at infinity ("Liouville manifolds") and which are diffeomorphic, but not symplectically isomorphic, to cotangent bundles T^*S^{n+1}, for any n+1 \geq 3. These manifolds are constructed as total spaces of Lefschetz fibrations, where the fibre and all but one of the vanishing cycles are fixed. We show that almost any choice of the last vanishing cycle leads to a nonstandard symplectic structure (those choices which yield standard T^*S^{n+1} can be exactly determined).

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