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 - snappy.computo...
Mathoverflow question (by Anton Petrunin) -
mathoverflow.n...
Anton Petrunin - anton-petrunin...
Michael Freedman - en.wikipedia.o...
Larsen Linov - math.berkeley....
Mathematics:
Hopf link - en.wikipedia.o...
Borromean rings - en.wikipedia.o...
Hyperbolic geometry - en.wikipedia.o...
Hyperbolic links - en.wikipedia.o...
bookstore.ams....
Linking number - en.wikipedia.o...
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" - users.monash.e...
Loom bracelets:
• Fishtail Loom Bracelet... - Fishtail Loom Bracelet - Tutorial || Rainbow Loom
• How to Make a Boxed Bo... - How to Make a Boxed Bow Bracelet - EASY design on the Rainbow Loom
• Rainbow Loom! DIY 5 Ea... - Rainbow Loom! DIY 5 Easy Rainbow Loom Bracelets without a Loom (DIY Loom Bands)