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Criticality for Ropelength of Knots and Links
Geometry/Topology| Speaker: | Rob Kusner, U of Massachusetts at Amherst |
| Location: | 693 Kerr |
| Start time: | Wed, Nov 5 2003, 4:10PM |
Description
We consider the problem of finding the shapes of tightly
knotted or linked ropes (tubes of uniform thickness around embedded
curves in 3-space). We will review recent work on minimization of
ropelength (the ratio of length over thickness) within an isotopy
class, especially its relation to classical invariants such as
crossing number, bridge number and various generalizations. Then we
will discuss a critical point theory for length of knotted or linked
curves subject to a thickness constraint. This leads to a "balance of
forces" criterion which characterizes critical configurations, and
in particular which lets us decide whether a putative minimizer is
legitimate.