Inhalt: In this lecture we will introduce some basic results on 3-manifolds, i.e. topological spaces locally modelled on Euclidean 3-space. There are two classical ways to study 3-manifold: By their embedded submanifolds of dimension 1 (knots) or dimension 2 (surfaces). Therefore, we will first study knots and surfaces by its own. Then we will move on to so-called structure theorems of 3-manifolds, which say that we can present and analyze 3-manifolds in simple combinatorial 2-dimensional graphics. In particular, we will prove that any 3-manifold admits a Heegaard spliting along a surface and an open book decomposition. Moreover, we will prove that any 3-manifold can be obtained by surgery along a link and as a 3-fold branched cover along a knot. This lecture is aimed at mathematics students (Bachelor and Master) with basic knowledge and interest in topology and can also be used as preparation for a thesis in the field of topology. *Prerequisites:* Prerequisites are the introductory lectures (Analysis I, II and Linear Algebra I, II) and basic notions from point set topology (covered in the module Topology I). Results from algebraic topology (fundamental group, homology theory) and differential topology are useful, but they are not needed for the understanding of the lecture.
Die Veranstaltung wurde 1 mal im Vorlesungsverzeichnis SoSe 2020 gefunden: