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Differential Geometry III:
Geometric Knot Theory
(Summer 2016)


This is an advanced course of the
Berlin Mathematical School
and will be held in English.
News
 [21.7.]
 Here are the slides from today's lecture.
 [18.7.]
 No lecture Tuesday 19 July; instead I recommend the
minisymposium Geometric Curvature Energies, 9:0011:00
in H2033, which is part of 7ECM.
 [4.7.]
 Exams for this course are available 25–27 July
 [22.6.]
 On 30 June there will be a special guest lecture by Myf Evans;
there is no lecture on 28 June.
 [8.5.]
 Oral exams
for last semester's courses will be offered on 20 May, 3 June and 10 June.
 [3.5.]
 The lecture on 10 May will be 10:00–11:00
 [8.4.]
 Lectures start on Monday 8.4.
Contents
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,
Convergence and
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,
Highresolution trefoil,
J. Phys. A 47, 2014, p. 285201.
Office hours
Thursdays, 13:30–14:30, MA 802
(see homepage for exceptions)
