The knot invariant Υ using grid homologies

According to the idea of Ozsváth, Stipsicz and Szabó, we define knot invariant [Formula: see text] without holomorphic theory, using constructions from grid homology. We develop a homology theory diagrams, show that text], as introduced this way, is well-defined invariant. reprove some important propositions new techniques, provides lower bound on unknotting number.