## Stable geometric dimension of vector bundles over
even-dimensional real projective spaces

Martin Bendersky, Donald M. Davis, and Mark Mahowald

This 23-page paper will appear in Transactions of the
American Math Society in 2005.

Abstract

In 1981, Davis, Gitler, and Mahowald determined the geometric
dimension of stable vector bundles or order 2^e over RP^{2n}
if n is sufficiently large and e \ge 75. In this paper,
we use the Bendersky-Davis computation of v1^{-1}pi_*(SO(m))
to determine this geometric dimension for all values of e
(still provided that n is sufficiently large). The same
formula that worked for e \ge 75 works for e \ge 6, but for
e<6 the formula is different due to anomalies in the formula
for v1^{-1}pi_*(SO(m)) when m \le 10.

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