### Cohomology in Everyday Life

#### Posted by David Corfield

I have been looking for examples, accessible to a lay audience, to illustrate the prevalence of cohomology. Here are some possibilities:

- Penrose’s impossible figures, such as the tribar
- Carrying in arithmetic
- Electrical circuits and Kirchhoff’s Law
- Pythagorean triples (Hilbert’s Theorem 90)
- Condorcet’s paradox (concerning the impossibility of combining comparative rankings)
- Entropy, but I think we never quited nailed this.

Anyway, I’d be grateful for any other cases of cohomology in everyday life.

There’s a related MathOverflow question on this. One of the answers notes a cohomological interpretation of mass. Following this up, I see Santiago García in Hidden invariance of the free classical particle writes that mass “has a cohomological significance, it parametrizes the extensions of the Galileo group.” Is this an interesting point of view?

## Re: Cohomology in Everyday Life

I’m happy with

Electrical circuits and Kirchhoff’s Law

but are the others really accessible to a LAY audience?

Perhaps Gauss’ linking number?