Knots in 4D


Knots in 4D


Erstellt von


Created by Ester Dalvit, 2016 at University of Toronto and University of Camerino.
Gefördert von: 
INdAM Fellowships in Mathematics and/or applications cofunded by Marie Curie Actions

4D-knots: what are they? Can we visualize them?
Are there interesting math problems about them?

The film is divided in three parts:

  1. Knots in 3D. Here we introduce notation and concepts for usual knots. 3D-knots are represented in 2D.
  2. Knotted surfaces in 4D. Parallel of part 1, in one dimension more! 4D-knots are represented as 3D objects (on a 2D screen, alas!).
  3. Ribbon knotted surfaces. A particular type of 4D-knots, maybe the “simplest” ones to describe. They have different representations and analyzing them we meet open questions in maths!


Part 1: Knots in 3D: https://www.
Part 2: Knotted surfaces in 4D: https://www.
Part 3: Ribbon knotted surfaces: https://www.


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