Contact Structures and Legendrian Links

Abstract

A contact structure on an oriented three-manifold is a maximally non-integrable 2-plane field distributed all over the three-manifold. Legendrian knots and Legendrian links in contact three-manifolds give important information about the contact three-manifold. A Legendrian knot/link is a knot/link which is everywhere tangent to the contact planes. In this thesis, the properties of Legendrian knots and links as well as the classification results are discussed. Legendrian unknots classification and Legendrian Hopf links classification in the contact 3-sphere S^3 are studied in detail.