Cube diagrams and 3-dimensional Reidemeister-like moves for knots

Abstract

In this paper we introduce a representation of knots and links called a cube diagram. We show that a property of a cube diagram is a link invariant if and only if the property is invariant under two types of cube diagram operations. A knot homology is constructed from cube diagrams and shown to be equivalent to knot Floer homology.

31 pages, 34 figures. Final version published by J. Knot Theory Ramifications