A strong non-immersion theorem for real projective spaces (Q1063913)

The following main result about non-immersability of real projective spaces improves upon many known ones and is very close to all others: Real projective space \(P^{2\ell}\) does not immerse into \({\mathbb{R}}^{4\ell-4d-2\alpha(\ell-d)}\), where d is the smallest nonnegative integer such that \(\alpha(\ell-d)\leq d+1\). The main ingredient of the proof, using BP-obstruction-theory as in the paper by \textit{L. Astey} [Q. J. Math., Oxf. II. Ser. 31, 139-155 (1980; Zbl 0405.55020)], is a calculation of \(BP2^*\) of a product of two projective spaces, where \(BP2=BP<2>\) is the Baas-Sullivan version of the Brown- Peterson-spectrum.