For n≥4, every complete connected smooth n-manifold with the quadratic-form lower bound −4Δ+Scal≥1 maps continuously to a simplicial complex of dimension at most n−2 with every fiber’s original-metric diameter bounded only by n.
For n≥4, every complete connected smooth n-manifold with the quadratic-form lower bound −4Δ+Scal≥1 maps continuously to a simplicial complex of dimension at most n−2 with every fiber’s original-metric diameter bounded only by n.
For n≥4, every complete connected smooth n-manifold with the quadratic-form lower bound −4Δ+Scal≥1 maps continuously to a simplicial complex of dimension at most n−2 with every fiber’s original-metric diameter bounded only by n.
If correct, strengthens the macroscopic-width theorem from pointwise to spectral scalar curvature.
Does a spectral scalar-curvature lower bound force uniform codimension-two width?
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