2 problems

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Conjecture on k-core metrics for manifolds constructed by plumbing
The $k$ -core metric conjecture. These manifolds in fact admit $k$ -core metrics with $k$ as given in these results.
Conjectureopencore-metrics plumbing positive-ricci-curvaturearXiv posted 2 days ago
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Neumann's diagonal plumbing conjecture for integral homology spheres
Neumann's conjecture. Some vertex of $dGamma$ has weight $1$ .
Conjectureopen3-manifolds intersection-forms plumbingarXiv posted 2 days ago

Conjecture on k-core metrics for manifolds constructed by plumbing