Universität Wien

250150 VO Low dimensional topology (2022W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
ON-SITE
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

as I said earlier, I will be organizing a winter school in Budapest in the end of January, and thus I won't be able to keep 2 of the classes on Jan 23 and on the 24th.

In the remaining classes, I want to talk about 4 manifolds and Kirby calculus and give you a taste of Heegaard Floer homology.

  • Monday 03.10. 09:45 - 11:15 Digital
  • Tuesday 04.10. 11:30 - 13:00 Digital
  • Monday 10.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 11.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 17.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 18.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 24.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 25.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 31.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 07.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 08.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 14.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 15.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 21.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 22.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 28.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 29.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 05.12. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 06.12. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 12.12. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 13.12. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 09.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 10.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 17.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 23.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 24.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 30.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 31.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

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.

Assessment and permitted materials

Oral exam after the end of the course.

If you would like to take an oral exam, then you should

-choose a topic that is about 3-4 lecture-worth of material,

-email me your topic choice and your wished dates for the exam,

-I will then approve your topic choice and suggest a concrete exam date and time,

-the exam can be held both in person or online, (I think in person is just a better experience for both of us, but I understand that online might work better for scheduling, so let's see).

Minimum requirements and assessment criteria

Examination topics

The contents of the course.

Reading list

Differential Topology:
>J. Milnor: Morse Theory

>Morris W. Hirsch: Differential Topology

knots:
>G. Burde, M. Heusener and H. Zieschang: Knots

3-manifolds:
>Allen Hatcher: Notes on Basic 3-Manifold Topology
https://pi.math.cornell.edu/~hatcher/3M/3Mdownloads.html

>Bruno Martelli: An introduction to Geometric Topology
https://people.dm.unipi.it/martelli/Geometric_topology.pdf

>Dale Rolfsen: Knots and Links

4-manifolds:
>R. Gompf und A. Stipsicz: 4-Manifolds and Kirby Calculus

Association in the course directory

MGEV

Last modified: Th 09.11.2023 11:48