Saturday, 16 June 2012

Cohomology for the layman (?)

Noticed this article over at n-Category Cafe: Cohomology in Everyday Life, where the author David Corfield asks for examples from everyday life to explain cohomology to a layman.

Given that the definition of cohomology (according to Wikipedia*)
In mathematics, specifically in algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a co-chain complex. That is, cohomology is defined as the abstract study of cochains, cocycles, and coboundaries. Cohomology can be viewed as a method of assigning algebraic invariants to a topological space that has a more refined algebraic structure than does homology. Cohomology arises from the algebraic dualization of the construction of homology. In less abstract language, cochains in the fundamental sense should assign 'quantities' to the chains of homology theory.
then he's got quite a challenge I think. However, of his current list of examples carrying in arithmetic is a good one and something that is familiar to everyone. If you're up to it then the mentioned paper by Daniel Isaksen: A Cohomological Viewpoint on Elementary School Arithmetic [1] is great reading.

Anyway, I look forward to what he finally presents - especially if he's going to present something about entropy which would give a nice link with information theory and, as we're talking about presenting to the layman, information privacy.


[1] Daniel C. Isaksen. (2002) A Cohomological Viewpoint on Elementary School Arithmetic. The American Mathematical Monthly, Vol. 109, No. 9. (Nov., 2002), pp. 796-805

*usual disclaimers apply of course.

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