Bott’s song

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.)

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© Tom Harris 2015–2018.

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