pseudocollarable

English

Etymology

From pseudo- +‎ collarable.

Adjective

pseudocollarable (not comparable)

1. (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.
   • 2015, Karim A. Adiprasito, Louis Funar, “Hyperbolicity of contractible manifolds”, in arXiv‎^[1]:

     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.