由Lutz、Martinet及Eliashberg的工作，我們可得知：若以同痕方式進行分類，在三維球面 上的切觸結構已經被分類完成。 本文將會藉由half及full Lutz twist方法，來為每一個同痕類找出更為具體且可算的代表元 素。;By the works of Lutz, Martinet and Eliashberg, we have known that the isotopy classes of contact structures on S^3 have been completely classified. In this thesis, we will find a representative for each class in a more explicit and computable form via the half and full Lutz twist.
