Immersing projective spaces in Euclidean space

Abstract

SynopsisUsing theKOℝ/2-theoretic obstruction theory developed in [4] and [5], necessary and sufficient conditions are derived for quaternionic projective spaces ℍPkand odd-dimensional complex projective spaces ℂP2k+1, of real dimensionmsay, to immerse in Euclidean space ℝ2m−1in the range l ≦ 14. The results refine those obtained by Davis and Mahowald ([10, 11]) and earlier authors.