The removal of the monarch and his court to the Brazils had tended to make the nobles less loyal in their inclinings […]
with thorns degloried
Modern sceptical historians are happy to write Dark Age history without naming kings and warleaders of the period, and it seems quite unjustified to take Gildas to task for doing the same thing.
Answering a question going back to Gromov, we show that, for an open, polyhedral contractible manifold M of dimension at least 6, the following conditions are equivalent: - M admits a geodesically complete CAT(0) metric; - M can be collapsed; - M is pseudocollarable. This yields many new contractible manifolds that admit CAT(0) metrics, and it shows that the CAT(0) property of a contractible manifold is purely determined by a condition at infinity, and shows that contractible manifolds of the Whitehead type can never admit a complete CAT(0) metric.
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