Pure Mathematics Knot Theory
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Knot Theory at Liverpool
Members and associates of the Research Group
Research Students
Previous Members
Publications
We maintain a
list of our publications,
which includes PostScript copies of some recent preprints.
There are also some
braid programs, mainly in Pascal, for calculating a number of knot invariants.
Areas of Interest
Hugh's interests include:
- Fibred knots and links.
- Braids and closed braid presentations of links.
- Satellite knots and links.
- Skein theory and quantum group link invariants.
- 3-manifold invariants.
- Vassiliev invariants.
- Applications to textiles.
Peter has worked mainly on the combinatorial aspects of knots. This has included
-
identifying the structure shared by the alternating and positive links to form
the more generalised class of homogeneous links.
-
relating topological properties to knot polynomials.
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finding techniques for identifying prime and simple knots.
Recent work has concentrated on arc-presentations of knots.
For an introduction to this area see the overview article in the
Warsaw Proceedings, 1995,
(
PostScript copy).
You may also enjoy his collection of material on the
Borromean Rings.
Victor's interests include:
- invariants (especially those of Vassiliev type) of Legendrian knots,
regular planar curves and planar wave fronts.
- Vassiliev type invariants of mappings.