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

Martin Bendersky, Hunter College, CUNY 10021,
mbenders@shiva.hunter.cuny.edu

Donald M. Davis, Lehigh University, Bethlehem, Pa. 18015
dmd1@lehigh.edu

55S40, 55R50, 55T15

Abstract: In a recent paper, the geometric dimension of all stable
vector bundles over real projective space P^n was determined if
n is even and sufficiently large with respect to the order 2^e of
the bundle.  Here we perform a similar determination when n is odd
and e>6.  The work is more delicate since P^n does not admit a
v1-map when n is odd.  There are a few extreme cases which we are
unable to settle precisely.