Subject: Question for the toplist
Date: Wed, 22 May 2002 17:15:15 +0200 (CEST)
From: darksfere
To: dmd1@lehigh.edu
On Mark Hovey's problem list
(available at
http://claude.math.wesleyan.edu/~mhovey/problems/elliptic.html)
there is the following question:
4. Yet another idea is to go back to a decription of cobordism I once
heard. I think this description is in print
somewhere, but I don't know where or who wrote it. I believe this idea
is a geometric description of MU^* X.
Think of X as a simplicial set. Over each vertex of X put a manifold.
Over each edge of X put a bordism
between the manifolds at the vertices. Over each triangle, put a
bordism between the bordisms on the
edges--I don't really know what these means, but orientation must be
involved. Continue in this way, and
that is an element of MU^* X. There must be some equivalence relation
you put on these, but I don't know
what it is. The problem would then be to figure out whether this works
and if it has been published, then to
determine how you get K-cohomology from this description--presumably
the bordisms between bordisms
go away, so are the identity, and this is the cocycle condition for
vector bundles. Then figure out how to get
elliptic cohomology.
Does anyone know about this description?
Is there any literature?
Thanks in advance,
Aydin Demircioglu
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