Date: Mon, 17 Jul 2000 15:06:44 -0500
From: William Singer <singer@murray.fordham.edu>
Subject: Atiyah-Hirz SS

Re the inquiry of Claude Schochet:

Let BU(2k,...\infty) be the 2k-1 connective cover of BU, and let
c_n be the n'th Chern class in the cohomology of BU.  One can
pull back c_n by the natural projection from BU(2k...\infty) to BU,
and ask about the divisibility of the resulting integral cohomology
class.  The answer is a number depending on n and k that is
computed in my paper, "Connective Fiberings over BU and U",
in Topology, 1968.  This result can be translated into a statement
about the order of the torsion hit by the differentials in the
Atiyah-Hirzebruch SS.


Bill Singer.