- 2003-04
>>Skift årstal- Knot Theory, 3-Manifolds and Quantum Invariants
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Knot Theory, 3-Manifolds and Quantum Invariants
3-4 hours of lectures per week.
Lecturer
Gregor Masbaum
Content
A knot is a simple closed curve in $3$-space, or, more generally, in
any $3$-dimensional manifold. Two such knots are considered equivalent
if one can be deformed into the other. Thus, knot theory is part of
topology: we are only interested in the topological properties of
knots. To show that two given knots are not equivalent one needs knot
invariants. A classical example of a knot invariant is the knot group
(the fundamental group of the complement of the knot). Other
invariants include the famous knot polynomials invented by Jones,
Kauffman, and others. These are called quantum invariants because of
their relationship both with quantum groups and with quantum field
theory. They can be generalized to quantum invariants of arbitrary
$3$-manifolds as well. The aim of the course is to give an
introduction to this rich and beautiful theory.
Prerequisite
Topologi 1
Literature
A literature list will be made available at start of the course
Evaluation
Students who do not intend to take a degree in Mathematics
or Statistics from the University of Aarhus, but wish to earn credits for
a 2.dels course from the Department of Mathematics, should indicate at
the beginning of the course that they wish to be examined.
The form of examination for these students will be active
participation together with oral or written contributions.
Credits
10 ECTS
Quarter
Spring 2004
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