Open Book Decompositions and Contact Surgeries

Abstract

By Alexander it was shown that an open book decomposition can be found for each closed, oriented 3-manifold. In this thesis, the importance of open book decompositions in terms of contact 3-manifolds will be studied by using surgery techniques. A closed curve in a 3-manifold that does not intersect itself is called a knot. Especially, knots which can be drawn on page of open book decompositions and boundary of open book decompositions will be studied in terms of topology and contact topology. The invariants of contact structures from open book decompositions will be studied.