Greg Egan on Nostr: The formal definition of the Burau representation is a bit daunting, but Vaughan ...

The formal definition of the Burau representation is a bit daunting, but Vaughan Jones gives a vivid intuitive description. If you think of a braid as a bowling alley with n lanes that can cross over and under each other, and at every crossing there is a probability t of a ball in the upper lane falling down to the lower lane, the (i,j) entry in the Burau matrix is just the probability that a ball starting in lane i exits in lane j.

[This metaphor only works for braids that can be built by stringing together any sequence of the “standard generators” where strand i crosses over strand i+1. To get the whole group you need to throw in the inverses of those generators as well.]