Heegaard Floer homology and alternating knots

• DOI: 10.2140/gt.2003.7.225
• Publication Date: 2005-06-15T15:44:45Z
• Authors: Peter Ozsváth; Zoltán Szabó
• Keywords: Floer Homology; Alexander polynomial; Knot polynomial; Knot complement; Khovanov homology; Tricolorability; Homology; Quantum invariant; Seifert surface; Jones polynomial

In an earlier paper, we introduced a knot invariant for null-homologous K in oriented three-manifold Y, which is closely related to the Heegaard Floer homology of Y. this paper investigate some properties these groups knots three-sphere. We give combinatorial description generators chain complex and their gradings. With help description, determine alternating knots, showing that special case, it depends only on signature Alexander polynomial (generalizing result Rasmussen two-bridge knots). Applications include new restrictions knots.