Does every Jordan curve in the Euclidian plane contain 4 points that form the corners of a square?
Starting from this old metric problem posed by Toeplitz a hundred years ago, we discuss problems in low-dimensional topology.
The talk will feature:
- knots, embedded circles in 3-dimensional space,
- disks and Möbius bands in 4-dimensional space, and
- a recent translation due to Hugelmeyer recasting Toeplitz' question as a problem about knots and Möbius bands.
No prior knowledge of low-dimensional topology will be assumed.