There are many deformable objects such as papers, clothes, and ropes in life space of a person. Robots need skills to manipulate deformable objects, in order to take active parts in such space. However, it is difficult for robots to manipulate deformable objects well and possibility of failure to operate deformable objects cannot be denied. Therefore, shape recognition method for deformable object manipulation is required, that has hyper degrees of freedom structures. Thus in this paper, we propose a description method of conditions of rope using a topological model and knot theory. And, we also propose a recognition method to obtain the structure of rope from sensor information through the CCD cameras when a robot manipulates a rope. The effectiveness of recognition method against a method using three-demensional data is verified through an experiment.