Subject: A question for the topology mailing list
From: Pascal Lambrechts
Date: Thu, 23 Nov 2006 12:06:20 +0100
Does anyone have a reference for the following result on the Bousfield-Kan
spectral sequence.
Take a cosimplicial space X^* seen as a diagram X^*: Delta --> Top.
Consider its n-th truncation X^*[n] obtained by restrinction the functor
to the subcategory Delta[n] of finite
ordered sets of cardinality <= n.
Let Y^* be the cosimplicial replacement of the diagram X^*[n].
Then the E2-page of the homotopy B-K spectral sequence for Y^* is
isomorphic to the homology of the homology of the n first columns of the
normalisation of the E1-page of the
homotopy B-K spectral sequence (normalized) of X^*.
We can prove this result but we guess that it is part of folklore and
would like to get a reference on that result or similar one in the
litterature.
Thanks,
Pascal
Pascal Lambrechts
pascal.lambrechts&uclouvain.be
Institut Mathématique
Chemin du cyclotron, 2
B-1348 Louvain-la-Neuve
BELGIUM
Phone +32 (0)10 473161