Low Dimensional Topology

June 13, 2014

Spaces of knots and low-dimensional topology

Filed under: Uncategorized — Ryan Budney @ 1:10 pm
Tags: , ,

Over the past 10-12 years, geometric topology has entered a new era.  Most of the foundational problems are solved, and there’s a fairly isolated collection of foundational problems remaining.  In my mind, the two most representative ones would be the smooth 4-dimensional Poincare hypothesis, and getting a better understanding of the homotopy-type of the group of diffeomorphisms of the n-sphere (especially for n=4, but for n large as well).   I want to talk about what I’d call second-order problems in low-dimensional topology, less foundational in nature and more oriented towards other goals, like relating low-dimensional topology to other areas of science.  Specifically, this is an attempt to describe the “spaces of knots” subject in a way that might entice low-dimensional topologists to think about the subject.

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