The Yamabe invariant of simply connected manifolds
classification
🧮 math.DG
keywords
connectedinvariantmanifoldsimplyyamabecurvaturedimensionequivalently
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We prove that the Yamabe invariant of any simply connected smooth manifold of dimension n greater than four is non-negative. Equivalently that the infimum of the L^{n/2} norm of the scalar curvature, over the space of all Riemannian metrics on the manifold, is zero.
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