Using topology to close a rubber band bracelet

With Sabetta Matsumoto and Saul Schleimer. It seems impossible, but you can make a giant loop out of lots of little (not very stretchy) loops. So you can wrap a broken suitcase using hair ties, without any cutting or knotting. Or you can finish off a rubber band bracelet without using a clip and, again, without any cutting or tying knots. We explain the problem, the solution, and some of the mathematics behind it all. Links and references: Snappy - computer program for analysing knots, links, and manifolds - Mathoverflow question (by Anton Petrunin) - Anton Petrunin - Michael Freedman - Larsen Linov - ~linov/ Mathematics: Hopf link - Borromean rings - Hyperbolic geometry - Hyperbolic links - Linking number - Milnor invariants - J. Milnor. Link groups. Ann. of Math. (2), 59:177–195, 1954 For an introduction to hyperbolic geometry and its application to knot theory we recommend Jessica Purcell’s book “Hyperbolic Knot Theory“ - ~jpurcell/ Loom bracelets: - Fishtail Loom Bracelet - Tutorial || Rainbow Loom - How to Make a Boxed Bow Bracelet - EASY design on the Rainbow Loom - Rainbow Loom! DIY 5 Easy Rainbow Loom Bracelets without a Loom (DIY Loom Bands)