Bordism und projective space bundles
Sven F\"uhring

TL;DR
This paper proves that total spaces of complex projective plane bundles generate the oriented cobordism ring, providing a new proof that certain simply connected manifolds admit positive scalar curvature metrics.
Contribution
It establishes that $CP^2$-bundles generate the oriented cobordism ring and offers an alternative proof of positive scalar curvature existence for specific manifolds.
Findings
$CP^2$-bundles generate the oriented cobordism ring
New proof of positive scalar curvature existence for simply connected non-spin manifolds
Connections between cobordism theory and scalar curvature results
Abstract
We prove that total spaces of -bundles generate the oriented cobordism ring . 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.
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Taxonomy
TopicsAdvanced Topics in Algebra
