Videos, and Games
Differential Geometry III:
Geometric Knot Theory
This is an advanced course of the
Berlin Mathematical School
and will be held in English.
- Here are the slides from today's lecture.
- No lecture Tuesday 19 July; instead I recommend the
minisymposium Geometric Curvature Energies, 9:00-11:00
in H2033, which is part of 7ECM.
- Exams for this course are available 25–27 July
- On 30 June there will be a special guest lecture by Myf Evans;
there is no lecture on 28 June.
- Oral exams
for last semester's courses will be offered on 20 May, 3 June and 10 June.
- The lecture on 10 May will be 10:00–11:00
- Lectures start on Monday 8.4.
Geometric knot theory studies the relationship between the geometry of a
simple closed curve in space and the topological knot type that it represents.
This course will cover various topics including the following: curves of
finite total curvature, the Fáry/Milnor theorem, knot energies and conformal
geometry of knots, Gromov's distortion, and tight knots and their ropelength.
Literature (more to be added later)
- Peter Cromwell, Knots and Links, Cambridge U.P., 2004.
- Burde, Zieschang, Knots, De Gruyter, 2nd ed., 2003.
- Colin Adams, The Knot Book, W.H. Freeman, 1994.
- Crowell, Fox, Introduction to Knot Theory, Springer (GTM 57), 1963.
- John M. Sullivan,
Curves of Finite
Total Curvature, in Discrete Differential Geometry,
Birkhäuser, 2008, pp. 137–161.
- Cantarella, Kusner, Sullivan,
On the Minimum Ropelength
of Knots and Links, Inventiones Math. 150:2,
2002, pp. 257–286.
- Burago, Burago, Ivanov, A Course in Metric Geometry, AMS (GSM 33), 2001.
- Denne, Sullivan,
isotopy type for graphs of finite total curvature,
in Discrete Differential Geometry,
Birkhäuser, 2008, pp. 163–174.
- Denne, Sullivan,
The distortion of a knotted
curve, Proc. AMS, 137, 2009, pp. 1139–1148.
- Denne, Diao, Sullivan,
Quadrisecants give new
lower bounds for the ropelength of a knot, Geom. Topol.
10, 2006, pp. 1–26.
- Cantarella, Kuperberg, Kusner, Sullivan,
The second hull of a knotted
curve, Amer. J. Math. 125:6, 2003, pp. 1335–1348.
- Przybyl, Pieranski,
J. Phys. A 47, 2014, p. 285201.
Thursdays, 13:30–14:30, MA 802
(see homepage for exceptions)