Abstract
A contact structure on a 3-manifold is a maximally non-integrable 2-plane field distributed
all over the 3-manifold. There are two types of contact structures on 3-manifolds:
tight and overtwisted. Knots that are everywhere tangent to the contact planes are called
Legendrian knots. In this thesis, we study basic techniques used in the classification
Legendrian knots. The aim of this thesis is to examine the techniques used in the classification
of Legendrian knots in tight contact manifolds and the techniques used in the
classification of Legendrian knots that have tight complements in overtwisted contact
manifolds. For this purpose, in this thesis we study the classification of Legendrian
unknots in contact 3-sphere S3 in detail.
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