Legendrian contact homology in the boundary of a subcritical Weinstein 4-manifold
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We give a combinatorial description of the Legendrian contact homology algebra associated to a Legendrian link in S1× S2or any connected sum #k(S1×S2), viewed as the contact boundary of the Weinstein manifold obtained by attaching 1-handles to the 4-ball. In view of the surgery formula for symplectic homology , this gives a combinatorial description of the symplectic homology of any 4-dimensional Weinstein manifold (and of the linearized contact homology of its boundary). We also study examples and discuss the invariance of the Legendrian homology algebra under deformations, from both the combinatorial and the analytical perspectives.
Published Version (Please cite this version)10.4310/jdg/1433975484
Publication InfoEkholm, T; & Ng, L (2015). Legendrian contact homology in the boundary of a subcritical Weinstein 4-manifold. Journal of Differential Geometry, 101(1). pp. 67-157. 10.4310/jdg/1433975484. Retrieved from https://hdl.handle.net/10161/17784.
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Eads Family Professor
My research mainly focuses on symplectic topology and low-dimensional topology. I am interested in studying structures in symplectic and contact geometry (Weinstein manifolds, contact manifolds, Legendrian and transverse knots), especially through holomorphic-curve techniques. One particular interest is extracting topological information about knots through cotangent bundles, and exploring relations to topological string theory. I have also worked in Heegaard Floer theory, quantum topology, and