Subject:
comment on N.Kuhn remark
From:
Alejandro Adem <adem@math.ubc.ca>
Date:
Fri, 11 Feb 2005 14:12:42 -0800 (PST)
To:
dmd1@lehigh.edu


This comment is about a construction Nick Kuhn recently mentioned:
------------------------------
Let V be a finite dimensional Z/2 vector space (and let
homology and cohomology have Z/2 coefficients).  There is a `universal'
central group extension  H_2(V) --> G(V) --> V whose d_2 differential in
the Serre spectral sequence for H^*(G(V)) is an isomorphism from
H2(V)=E_2^{0,1} to E_2^{2,0}=H2(V).
--------------

The groups described by Nick are known as universal W-groups, and have been studied by Minac and Spira in applications to Galois cohomology. Calculating their mod 2 cohomology is an interesting open problem (see math.AT/9812169).

The mod p analogues have also been studied; their cohomology can be completely computed if p is large enough with respect to the dimension of V (see math.AT/0008229).

And yes, they are pC groups.

Alejandro Adem.