Subject: RE: 2 questions
Date: Sat, 5 Oct 2002 15:06:00 +0800
From: "Berrick A J"
To: "Don Davis"
Dear Don,
A response to Tom Goodwillie's question (assuming I've correctly read an old paper of mine). Applying the plus-construction to K(G,1) for the torsion-free group G below yields K(Z,2) . So G has the required cohomology ring, more generally than just over the integers.
The group G is a split extension of groups as follows. Let Q' be the linearly ordered set of rational numbers strictly between 0 and 1 , and let A be the group of all finitely supported functions from Q' to Z (infinite cyclic group). Then the split extension defining G has as kernel A x A and as quotient the upper-unitriangular group of integral matrices whose entries are indexed by the order Q' .
For further details and arguments, see
A J Berrick: Two functors from abelian groups to perfect groups, J Pure Applied Algebra 44 (1987), 35-43.
Best regards,
Jon.
_____________________________________________________________________
Prof A J Berrick
Department of Mathematics Tel. : +65 6874 2747
National University of Singapore Fax : +65 6779 5452
2 Science Drive 2
Singapore 117543 Email: berrick@math.nus.edu.sg
SINGAPORE http://www.math.nus.edu.sg/~matberic/
_____________________________________________________________________
-----Original Message-----
From: Don Davis [mailto:dmd1@lehigh.edu]
Sent: Thursday, October 03, 2002 8:44 PM
To: (Don Davis)
Subject: 2 questions
Two new questions posted today..........DMD
_________________________________________________
Subject: question for list
Date: Wed, 2 Oct 2002 12:15:53 -0400 (EDT)
From: Tom Goodwillie
Is there a torsion-free discrete group G such that the
integral cohomology ring of BG is isomorphic to that of
infinite complex projective space?
Tom Goodwillie
___________________________________________________
Subject: question for discussion list
Date: Wed, 2 Oct 2002 17:54:27 -0700 (PDT)
From: Igor Belegradek
Let M be a boundary component of a cobordism W such that the
inclusion M-->W is r-connected. It is known that if rr.
(See e.g. C. T. C. Wall, Geometrical connectivity I, J. London.
Math. Society., 3, (1971), 597-604).
Is the bound r