Meaning of pseudocollarable | Babel Free

Definitions

Such that there exists a neighborhood that is homeomorphic to a product, but this homeomorphism may not preserve all the desired structures or conditions that a true collar neighborhood would.

not-comparable

Examples

“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.”

CEFR level