Symplectic homology of 4-dimensional Weinstein manifolds and Legendrian homology of links

Symplectic homology of 4-dimensional Weinstein manifolds and Legendrian homology of links

Tue, 11/05/2010
15:45 		Tobias Ekholm (Uppsala) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Symplectic homology of 4-dimensional Weinstein manifolds and Legendrian homology of links
We show how to compute the symplectic homology of a 4-dimensional Weinstein manifold from a diagram of the Legendrian link which is the attaching locus of its 2-handles. The computation uses a combination of a generalization of Chekanov's description of the Legendrian homology of links in standard contact 3-space, where the ambient contact manifold is replaced by a connected sum of $ S^1\times S^2 $'s, and recent results on the behaviour of holomorphic curve invariants under Legendrian surgery.