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Dror Bar-Natan:
Talks:
# Knots in Three and Four Dimensions

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### September 25, 2015

**Abstract.** Much as we can understand 3-dimensional objects by staring
at their pictures and x-ray images and slices in 2-dimensions, so can we
understand 4-dimensional objects by staring at their pictures and x-ray
images and slices in 3-dimensions, capitalizing on the fact that we
understand 3-dimensions pretty well. So we will spend some time staring at
and understanding various 2-dimensional views of a 3-dimensional elephant,
and then even more simply, various 2-dimensional views of some
3-dimensional knots. This achieved, we'll take the leap and visualize some
4-dimensional knots by their various traces in 3-dimensional space, and
if we'll still have time, we'll prove that these knots are really knotted.

**Talk video:**