Bott’s song

Topics:
travel, maths

I’m back in Southampton after a great week in Strasbourg, where I learned a lot and also met some nice people who I hope I’ll stay in touch with.

As one would expect from a masterclass on topological K-theory, a recurring
theme was the following 8-periodic sequence of groups:

`\mathbb{Z} / 2 \ \ \mathbb{Z} / 2 \ \ 0 \ \ \mathbb{Z} \ \ 0 \ \ 0 \ \ 0 \ \ \mathbb{Z}.`

I remember somewhere seeing this sequence referred to as ‘Bott’s song’.
It doesn’t seem to be in common usage, but I think it’s a charming name and I
hope it catches on. And if the *KO** tune proves too hard to follow,
there’s always *KU**, Bott’s song for beginners:

`\mathbb{Z} \ \ 0`

(repeat).

**EDIT** I’ve since been informed by
Carl McTague that Bott’s song goes to the
tune of *Twinkle Twinkle Little Star*:

zee-two, zee-two, zero, zee, zero, zero, zero, zee

(It sounds better sang in American.)