The Yamabe invariant of simply connected manifolds

DOI10.1515/crll.2000.049zbMath0949.53026arXivmath/9808062OpenAlexW2964096677MaRDI QIDQ4488492

Jimmy Petean

Publication date: 5 July 2000

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9808062

zbMATH Keywords

cobordismsurgeryYamabe invariantSigma constant

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Critical metrics (58E11) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (14)

Connected sums with \(\mathbb{H} P^n\) or \(CaP^{2}\) and the Yamabe invariant ⋮ Isoperimetric regions in spherical cones and Yamabe constants of \(M \times S^{1}\) ⋮ Smooth Yamabe invariant with boundary ⋮ Collapsing manifolds obtained by Kummer-type constructions ⋮ Computations of the orbifold Yamabe invariant ⋮ Compactification on negatively curved manifolds ⋮ The Yamabe invariants of Inoue surfaces, Kodaira surfaces, and their blowups ⋮ Highly connected manifolds of positive $p$-curvature ⋮ Unstable Einstein metrics ⋮ On entropies, \(\mathcal {F}\)-structures, and scalar curvature of certain involutions ⋮ The Yamabe invariant ⋮ Low-dimensional surgery and the Yamabe invariant ⋮ On area comparison and rigidity involving the scalar curvature ⋮ Some examples of vanishing Yamabe invariant and minimal volume, and collapsing of inequivalent smoothings and PL-structures

Cites Work

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• Compact 8-manifolds with holonomy \(\text{Spin}(7)\)
• Simply Connected Spin Manifolds with Positive Scalar Curvature

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