Immersions of \(RP^{2^{e} - 1}\) (Q945647)

The main theorem (Theorem 1.1) states that if \(e\geq 7\), then the real projective \((2^e-1)\)-space can be immersed in the real euclidean \((2^{e+1}-e-7)\)-space. For \(e\geq 14\), this result improves by 1 the previously known immersibility results of real projective spaces [\textit{R. J. Milgram}, Ann. Math. 85, 473--482 (1967; Zbl 0171.22203)] and [\textit{D. Davis} and \textit{M. Mahowald}, Trans. Am. Math. Soc. 236, 361--383 (1978; Zbl 0341.57005)]. The best-possibility of the result is still open. The authors adopt an induction on geometric dimension in the proof, where compatibility of liftings is essential. The proof is long (31 pages), but the methods used are not new.