Please, register
with Moodle for this class.
Literatur:
1. R.H.Crowell
and R.H. Fox: Introduction to Knot Theory, Springer 1963
(electronically available in library - you have to use HU-VPN!)
2. W.B.R. Lickorish: An Introduction to Knot Theory, Springer
1997
(electronically available)
3. G.Burde, H.Zieschang, M.Heusener: Knots. De Gruyter 2014
(electronically available)
4. M.A.Armstrong: Basic Topology. Springer 1983 (electronically
available)
5. Ch. Livingston: Knot Theory. MAA 1993 (electronically available,
also in German)
6. V.V. Prasolov, A.B. Sossinsky: Knots, Links, Braids and 3-Manifolds.
AMS 1991 (electronically availabe)
7. C.C. Adams: On Knots, AMS 2004 (no electronic version available)
8. C. Kassel, O.Dodane, V. Turaev: Braid Groups, Springer 2008
There are many more (have a look in the library catalogue).
There is a class on 3-Manifolds by Marc Kegel which is
closely related to Knot theory!
Talks
05/06 Knots: Definition, Examples (also pathological ones), Links
(Lit.: 1., 2., 3.,5.)
Todoulou
05/13 Knot diagrams (definition and existence), Reidemeister moves
(including proofs) (1., 2., 3., 5.)
Huneshagen
05/20 Idea
of knot invariants. Bridge and unknotting numbers (short discussion).
Linking number. Tricolourability (definition, proof of
invariance)(internet research)
Gerlach
05/27 Knot polynomials (combinatorial definition of Alexander-Conway
polynomial (and possibly the Jones polynomial))
Dawid
06/03 Seifert surfaces (Proof of existence). Genus of a knot,
additivity under knot sums, prime decompositon of knots (3., 4., 5.)
Levinson
06/10 Fundamental group (definition, group axioms), fundamental group
of a circle
Mousseau
06/17 Knot group (representation of the fundamental group of the knot
complement via knot diagrams)
Đukić
06/24 Cyclic coverings
and the commutator subgroup of the knot group Mohnke
07/01
Fibered knots/links El Agami
07/08 Universal cyclic coverings, geometric definition of the Alexander
polynomial
07/22 Braid groups, Bureau representation and the Alexander-Conway Polynomial (8.) Maravall
last changes: Thu, July 22, 7:05 p.m.