Subject: question for the list
Date: Wed, 29 May 2002 13:35:48 -0700
From: John H Palmieri <palmieri@math.washington.edu>

In general, what is known about the cohomology of torsion-free groups?
(More precisely, I should say, "the continuous mod p cohomology of a
non-compact torsion-free topological group".)  For instance, in the
compact case, this algebra consists entirely of nilpotent elements;
what about in the non-compact case?

Fix a prime p.  The particular group I'm interested in is an inverse
limit of infinite groups:

  G = lim ( ... --> G_3 --> G_2 --> G_1 )

G_1 is the algebraic closure of the field with p elements, under
addition.  Each map G_n --> G_{n-1} is onto, with kernel isomorphic to
G_1.  Each G_n has torsion, but the limit does not.  Also, each G_n is
discrete.

Actually, I can define such an inverse limit over any field; over a
finite field, the result is a profinite group, and I think my group G
is a suitable direct limit (with respect to n) of the profinite groups
associated to F_{p^n}.

Regardless, I would like to know something about the cohomology of G.

--
John H. Palmieri
Dept of Mathematics, Box 354350    mailto:palmieri@math.washington.edu
University of Washington           http://www.math.washington.edu/~palmieri/
Seattle, WA 98195-4350