A strong non-immersion theorem for real projective spaces. (English) Zbl 0574.57014

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 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.
Reviewer: M.Raussen


57R42 Immersions in differential topology
55S40 Sectioning fiber spaces and bundles in algebraic topology
55P42 Stable homotopy theory, spectra
55N35 Other homology theories in algebraic topology
55N20 Generalized (extraordinary) homology and cohomology theories in algebraic topology
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