On nonimmersion of real projective spaces. (Q1421996)

The author proves that if \(n=2^r+2^s\;(s\geq 0)\), then the real projective \((16n+11)\)-space \(P^{16n+11}\) cannot be immersed in euclidean \((32n+12)\)-space \(\mathbb{R}^{32n+12}\). This result is the best possible, because Theorem 5 for \(t=1\) of \textit{J. Adem}, \textit{S. Gitler}, and \textit{M. Mahowald} [Bol. Soc. Mat. Mexicana 10, 84--88 (1965; Zbl 0152.40804)] implies that \(P^{16n+11}\) can be immersed in \(\mathbb{R}^{32n+13}\). The method used there is similar to that employed by \textit{D. M. Davis} and \textit{V. Zelov} [Proc. Am. Math. Soc. 128, No. 12, 3731--3740 (2000; Zbl 0951.57013)].