Subject: Re: clarification on question
From: Peter Landweber
Date: Thu, 28 Jun 2007 17:46:44 -0400
Kevin,
Konstantin Mischaikow is now at Rutgers, so I know his use of cubical
homology. In addition to the book he has written with his coauthors, you
can probably locate some articles they have written on cubical homology
(and so also cohomology). You can certainly think of this as cellular
homology and cohomology, where cubes of various dimensions are the cells;
thus you can cite your favorite source for cellular (co)homology.
Peter Landweber
> 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).
>