250116 VO Introduction to knot theory (2016S)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Friday 04.03. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Friday 18.03. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Friday 08.04. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Friday 15.04. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Friday 22.04. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Friday 29.04. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Friday 06.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Friday 13.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Friday 20.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Friday 27.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Friday 03.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Friday 10.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Friday 17.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Friday 24.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 29.06. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The object of study in knot theory is at the same time intuitive and part of our every day experience as well as very complicated and linked to abstract and deep mathematical concepts. A mathematical knot is an embedding of the circle into three-space, considered up to isotopy.

In this course we see how complicated it is to classify knots and we learn about different kinds of knot invariants, in particular the Jones and Alexander polynomials. The more recent developments of quantum invariants via Hopf algebras are introduced. To obtain a systematic understanding of knot invariants, we learn about the concept of finite type invariants and the combinatorial description of these. If time permits we discuss relations to 3-manifold invariants.

Required knowledge:
All topological concepts will be explained. Basic group theory and algebra is helpful but can be acquired during the course.

Assessment and permitted materials

Minimum requirements and assessment criteria

Examination topics

Reading list

Association in the course directory

MGEV, MALV

Last modified: Mo 07.09.2020 15:40