Sunday 12 November 2006

Axiomatic Sheaf cohomology/Aural Objets Trouves

... Updates, updates... Well, right now I've learnt the axioms of axiomatic sheaf cohomology. Which is nice. The only problem is that everything is rather esoteric at the moment - apparently every fine torsionless resolution of the constant sheaf defines canonically a sheaf cohomology theory. Not only that, but later in the book, it proves that every sheaf cohomology theory is isomorphic for the same choice of the base principal ideal domain K (the sheaves are sheaves of K-modules). This seems nuts right now, but I guess it must be a little less crazy than it sounds. Actually a sheaf cohomology theory seems to be rather a big beastie and so if you pick K as the field of real numbers, the cohomology theory that you get must encapsulate all the classical cohomology theories like de Rham and Cech. Crazy eh? On a lighter note, I found out about an awesome experimental music project called Milkcrate. The idea of the whole thing is to make, I guess, unconventional music. It's awesome. The rules are essentially that all of the objects that you use have to be explicitly non-musical (egg cartons and yoghurt pots?) and they have to all fit inside a standard - presumably Australian - milkcrate. Oh, and it all has to be completed in 24 hours. It seems to me that this is bringing the idea of objets trouves to music in a whole new electronic way. Hurrah for the internet! (see http://www.milkcrate.com.au/)