Contact blow up and cylindrical contact homology of toric contact manifolds of Reeb type

Abstract

Let (V, ξ) be a toric contact manifold of Reeb type that is a prequantization of a toric symplectic manifold (M, ω). A contact blow up of (V, ξ) is the prequantization of a symplectic blow up of (M, ω). Thus, a contact blow up of (V, ξ) is a new toric contact manifold of Reeb type. In some special cases we are able to compute the cylindrical contact homology for the contact blowup using only the cylindrical contact homology of the contact manifold we started with.