arXiv subjects
Publications and source records attributed to Sven Führing.
We prove that total spaces of $CP^2$-bundles generate the oriented cobordism ring $Ω_*$. Combined with the surgery lemma this yields a somewhat different proof of Gromov's and Lawson's theorem that all simply connected non-spin manifolds of dimension $\geq$ 5 carry a metric of positive scalar curvature.
Let $M$ be a smooth closed spin (resp. oriented and totally non-spin) manifold of dimension $n\geq 5$ with fundamental group $π$. It is stated, e.g. in [RS95], that $M$ admits a metric of positive scalar curvature (pscm) if its orientation class in $ko_n(Bπ)$ (resp. $H_n(Bπ;\Z)$) lies in the subgroup consisting of elements which contain pscm representatives. This is 2-locally verified loc. cit. and in [Sto94]. After inverting 2 it was announced that a proof would be carried out in [Jun], but this work has never appeared in print. The purpose of our paper is to present a self-contained proof of the statement with 2 inverted.