Subject: Still about cubical cohomology reference
From: Kevin Iga
Date: Thu, 28 Jun 2007 00:32:01 -0700
Thank you for all the people who responded. I am looking up some of these
references now, but as I have gone through some of them, I should clarify
what I am looking for. For instance, I checked out Serre's thesis but
unfortunately it's not what I need. His cubical cohomology is a variant
of SINGULAR cohomology, not SIMPLICIAL cohomology. For Serre, chains are
generated by maps from a standard cube into the space (a sort of singular
cubical homology results). What I need is a notion of a cubical complex
(by analogy to a simplicial complex), where the chains are generated by
the cells of the complex. This is more combinatorial, and the chain
groups are finite dimensional. In my case, I have a polytope made up of
cubes and I am actually working on the cochain level explicitly (this
turns out to classify certain aspects of representations of a certain Lie
superalgebra).
As I have not finished looking through everyone's suggested references, it
may be that some of them may be what I need. But since many
misinterpreted my request, I thought I'd clarify.
Kevin Iga