Some Research On The Tunnel Of A Sort Of Two Bridge Knots

In this paper , I will study a sort of knots which is embedded in the solid torus. This knot have a special relation with the two bridge knots in three sphere S 3.The Japanese mathmatician Kobayashi have done a sophiscated research on unknotting tunnel for two bridge knots, and completed the work of the classification of unknotting tunnel for two bridge knots.We can regard the knot this paper considered as the two bridge knots embedded in the solid torus,and have the same property with the two bridge knots in S 3. Based on the work of formers such as Kobayashi, we use the fact that the Heegaard splittings of solid torus is standad and the completed list of unknotting tunnels for two bridge knots, make an invesgation on the tunnels of the special knot embedded in solid torus, and get some result on its tunnels, and prove that these tunnels cann't be unknotting tunnels for these knots.This paper consist of three chapter.The first chapter is introduction,consist of the background of research and the original of this title.The second chapter is prelimilary,we give the concepts and results which we needed in the later chapter. .The last chapter is the main chapter of this paper, we worked out some result on the tunnels for two bridge knot embedded in solid torus.