On Symplectic Cobordisms

Four-dimensional symplectic cobordisms containing three-handles

We construct four-dimensional symplectic cobordisms between contact threemanifolds generalizing an example of Eliashberg. One key feature is that any handlebody decomposition of one of these cobordisms must involve threehandles. The other key feature is that these cobordisms contain chains of symplectically embedded two-spheres of square zero. This, together with standard gauge theory, is used ...

Symplectic Cobordisms and Open Book Decompositions

A Legendrian surgery presentation of contact 3–manifolds

We prove that every closed, connected contact 3–manifold can be obtained from S 3 with its standard contact structure by contact (±1)–surgery along a Legendrian link. As a corollary, we derive a result of Etnyre and Honda about symplectic cobordisms (in slightly stronger form). MSC: Primary 53D35; Secondary 57R65, 57R90

Automatic Transversality and Orbifolds of Punctured Holomorphic Curves in Dimension Four

We derive a numerical criterion for J–holomorphic curves in 4–dimensional symplectic cobordisms to achieve transversality without any genericity assumption. This generalizes results in [HLS97] and [IS99] to allow punctured curves with boundary that generally need not be somewhere injective or immersed. As an application, we combine this with the intersection theory of punctured holomorphic curv...

Transversality theory, cobordisms, and invariants of symplectic quotients

This paper gives methods for understanding invariants of symplectic quotients. The symplectic quotients that we consider are compact symplectic manifolds (or more generally orbifolds), which arise as the symplectic quotients of a symplectic manifold by a compact torus. A companion paper [23] examines symplectic quotients by a nonabelian group, showing how to reduce to the maximal torus. Through...