Description
We can find braids - made of hair, leather, silk, rope, gold or bread - in human cultures all over the world and and throughout history. They are also not hard to describe algebraically, and naturally form groups, which we shall study in some detail.Braids are related to knots and links, and you will be able to draw on the first half of Geometric Topology II. Braid-like structures also occasionally arise in nature (convection, DNA, even the rings of Saturn), and certain hard questions about braids can be used (in a similar role to the factoring of very large numbers) in cryptography.
This topic may appeal to you if you like to be able to represent abstract ideas visually, and argue using diagrams as well as notation. It is suitable for several students.