Construction Of Hopf Polyhedral Links And Their Topological Properties

DNA has been considered to be the main genetic material, and nanotechnology provides technical support in controlling and using DNA. In the past decades, a lot of three-dimensional structures of DNA were synthesized in the laboratory. These structures has broken away from the traditional chemical and biological structures, and brought a challenge to the theory of chemistry. Establishment a theoretical model, the construct method and topological properties are very important. The contents of this thesis include:1. Classify the DNA polyhedron and summarize the synthetic mechanism. In addition, a simple introduction of protein and RNA polyhedron will be made.2. Build polyhedral link which is consistent with star DNA polyhedron structure, and study its constructing method.3. Surface construction method is proposed by breaking the traditional building method of polyhedral link. The process to constructthe several polyhedral link by surface construction method will be illustrated.4. Starting from the knot and polyhedra, the topological properties of polyhedral link were discussed and summarized. The applicative scope of new euler’s formula in Hopf polyhedral links will be suggested.This thesis is based on DNA polyhedra synthesized by experiments, the kont theory and polyhedral theory. It explored and expanded polyhedral link theory by developing a new method. It hopes that the results of this paper can provide new ideas and goals for DNA or protein synthesis.