2013/07/31 by Tobias Ekholm, Lenhard Ng · 2 citations
Mathematics · #math.SG #math.GT #msc:53D42 #msc:57R17 #msc:57M27
published as J. Differential Geom. 101 (2015), no. 1, 67-157 · v2: 88 pages, incorporated referee suggestions
arxiv created 2014/09/16 · arxiv updated 2015/09/01
We give a combinatorial description of the Legendrian contact homology algebra associated to a Legendrian link in S1× S2 or 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.