Note Of Diagram Of Alternating Knots

This paper discusses the relationship between the alternating knot and the Heegaard surface.Specifically,it gives a conditions for how to make the alternating knot embedded onto the Heegaard surface with a genus of 2.This paper also gives a way to embed the alternating knot onto the corresponding genus Heegaard surface.The main arrangements are as follows: The first chapter introduces the development of knots theory.The second chapter introduces some definitions which required in this paper.The third chapter and first section mainly solved the problem how to describe the alternating knots that min{W,B} = 3.The second section shows how to make the few knots embedded in a surface.From those example,we can guess the minimum genus of the surface is equal to min{W,B}-1.The third section gives way to judge whether the knot has chirality or not through the relationship of blacks block and white blocks.