Invariants in contact topology
It is known that all 3-dimensional contact manifolds are divided into two complementary classes: tight and overtwisted. The overtwisted contact structures on 3-manifolds are classified up to isotopy by their formal homotopy classes. Until very recently, there was known only one result allowing to distinguish contact structures on manifolds of dimension \(> 3\) within a given formal homotopy class: for any \(n > 2\), the sphere \(S^{2n-1}\) has a contact structure \(\xi_1\) in the standard formal homotopy class, which is not isomorphic to the standard structure \(\xi_0\). The main goal of this paper is the construction of new algebraic invariants, related to Gromov-Witten invariants of symplectic manifolds, which would allow to distinguish contact manifolds in the same formal homotopy class. For this purpose, the graded contact homology algebra of a contact manifold \((V,\xi)\) is constructed and investigated.
scientific article; zbMATH DE number 1184332