Bordism und projective space bundles

2020/06/27 by Führing, Sven
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2006.15394

Abstract

We prove that total spaces of CP²-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 ≥ 5 carry a metric of positive scalar curvature.

Related

• Parametrized Morse Theory and Positive Scalar Curvature
• Cobordism Invariance of the Homotopy Type of the Space of Positive Scalar Curvature Metrics
• Topology of non-negatively curved manifolds
• The positive scalar curvature cobordism category
• Bordism categories and orientations of gauge theory moduli spaces