Subject: Re: response & 2 questions
Date: Wed, 8 May 2002 17:47:23 -0400
From: Vince Giambalvo <vince@math.uconn.edu>
To: dmd1@lehigh.edu

Don,
I don't know too much about the history of X<n>, but
the following math review is certainly old.

38 #5206 55.30
Giambalvo, V.
The ${\rm mod}$ $p$ cohomology of ${\rm BO}\langle 4k\rangle $.
Proc. Amer. Math. Soc. 20 1969 593--597.

Let BO denote the classifying space for stable vector bundles, and
$\text{BO}(4k)$ its $4k-1$ connective covering. Using some methods and
results of the reviewer [Topology 7 (1968), 271--303; MR 38 #717], the
author computes the cohomology rings $H\sp *(\text{BO}(4k),Z\sb p)$
for $p$ an odd prime. (For the case $p=2$ these rings have been
determined by R. Stong [Trans. Amer. Math. Soc. 107 (1963), 526--544;
MR 27 #1944].)

   Vince