Complexity of Seifert manifolds

In this thesis, we give an overview over the theory of Seifert fibre spaces and the complexity theory. We start by giving some preliminary notions about 2-dimensional orbifolds, fibre bundles and circle bundles, in order to be able to understand the following part of the thesis, regarding the theory of Seifert fibre spaces. We first see the definition and properties of Seifert fibre spaces and, after giving a combinatorial description, we classify them up to fibre-preserving homeomorphism and up to homeomorphism. Afterwards, we introduce the complexity theory, at first in a general way concerning all compact 3-manifolds and then focusing ourselves on the estimation for the complexity of Seifert fibre spaces. We also give some examples of spine constructions for manifolds with boundary having complexity zero.