250116 VO Introduction to knot theory (2016S)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Wednesday 29.06.2016 Tuesday 13.09.2016 Saturday 09.05.2020

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