SINGULARITIES AND SOME INVARIANTS OF SINGULARITIES IN CONTACT 3-MANIFOLDS

Abstract

In this paper, we study the singularities in contact 3-Manifolds. We give simple presentations for singularities, make an initial classification of them and show that the space of all singularities has continuous moduli. We also study the stabilities of singularities and obtain that a nondegenerate singular point is isolated. Finally, by means of the transversality theorem of Thom, we show that generically every immersion contains no degenerate singular points. Thus the singular set of a closed surface is finite.