... denote the corresponding holomorphic map to Σ. Since D(φ) has only 0 and 1 coefficients, it follows HOLOMORPHIC DISKS AND THREE-MANIFOLD INVARIANTS1197 and β, resp. ξ and ξ. In view of Proposition ... here re-quire no gauge theory to define and calculate, only pseudo -holomorphic disks in the symmetric product. Indeed, in many cases, such disks boil down to holomorphic maps between domains in Riemann ... audience.2. Basic properties We collect here some properties ofHF, HF+, HF−, and HF∞whichfollow easily from the definitions.2.1. Finiteness properties. Note thatHF and HF+distinguish...