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A movie on knotted surfaces in 4-space
by
Ester Dalvit
University of Toronto
I will show a computer graphics movie about knotted surfaces in 4-dimensional space.
The purpose of the movie is twofold: to explain topics in knot theory in an informal and charming way to non-experts, and to provide images and animations to experts for teaching and popularization.
Contents: An introduction to knots (2d knot diagrams, Reidemeister moves, 3-colorability); The corresponding theory for knotted spheres in 4-space (3d surface diagrams, Roseman moves, 3-colorability); Ribbon 2-knots, welded knots, Satoh's Tube map relating the two, a conjecture about a Reidemeister calculus for ribbon knotted surfaces.
The movie is still work in progress. Drafts can be found at http://katlas.math.toronto.edu/ester/movies/
Date received: April 25, 2016
Copyright © 2016 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbmk-42.