Bordism und projective space bundles

Abstract

We prove that total spaces of $C{P}^2$-bundles generate the oriented cobordism ring ${\Omega }_{\ast }$. 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 $\ge$ 5 carry a metric of positive scalar curvature.

Cited by in corpus (1)

• On the homotopy type of the space of metrics of positive scalar curvature