Groping Around in 4-Dimensions Using von Neumann Algebras


Tim Cochran

Rice University (visiting MIT)

Brandeis University

Thursday, October 21, 2004


Talk at 4:30 p.m. in 317 Goldsmith Hall

Tea at 4:00 p.m. in 300 Goldsmith Hall


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.

Home Web page:  Alexandru I. Suciu  Posted: April 6, 2004 
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