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Abstract:
The talk will be about knot theory and how certain very topological
questions can be answered with the help on noncommutative algebra and
functional analysis. We approach the classical question: When does a
knotted circle in the 3-sphere bound a 2-dimensional disk in the
4-ball? We "filter" this question by asking when such a knot is the
boundary of a "Grope" of height n. A Grope is a generalization of a
surface and has been quite useful in topology lately. These notions
will be discussed. After reviewing the history of this problem, we will
indicate how noncommutative algebra and von Neumann algebras arise
naturally.
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