Abstract
We prove that in many cases the geometric dimension of the p-fold Whitney sum p1Hk of the Hopf bundle Hk over quaternionic projective space QPk is the smallest n such that for all i < k the reduction of the ith symplectic Pontryagin class of pHk to coefficients 74i-1((RP /RRPn1 ) A bo) is zero, where bo is the spectrum for connective KO-theory localized at 2. We immediately obtain new immersions of real projective space RP4k+3 in Euclidean space if the number of I's in the binary expansion of k is between 5 and 8.
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