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Pronunciation varies by accent · adjective
(mathematics) 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..
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.
Use pseudocollarable when its meaning, tone and grammar fit the full sentence. A synonym is not always a direct replacement.
Pseudocollarable means (mathematics) 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..
The closest synonym depends on the sentence and intended sense.
The opposite depends on the specific sense.
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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