250150 VO Low dimensional topology (2022W)

Zoom Link for the first 2 lectures:
https://univienna.zoom.us/j/6219689264?pwd=YzNEMkRCMkFSbUZWVzVpUmdXaEUvZz09

Meeting ID: 621 968 9264
Passcode: torus

Low dimensional topology is the study of (smooth) 3- and 4- dimensional manifolds (=spaces that can be modelled on the Euclidian 3- or 4-space). A classical way of studying 3-manifolds is by understanding embedded submanifolds: knots and surfaces.

Thus as a warm-up, we will spend some lectures on knots in the 3-space.

We will then briefly introduce notions and constructions from Differential Topology concentrating on Morse theory and its consequences. And use surfaces (2-dimensional manifolds) as basic examples.

We will then move on to the study of 3-manifolds by first giving some constructions, and then understanding the specifics of the Algebraic Topological invariants of 3-manifolds. Next, we will decompose 3-manifolds into simple pieces first along spheres and then tori. We then discuss Dehn surgery along knots, as a specific construction.

As a reformulation of Morse theory, we will give a compact description of 4-manifolds called Kirby diagrams, and discuss Kirby calculus.

If time permits we will briefly discuss recent methods to study 3- and 4-manifolds.