Coarse embeddings of metric spaces into Banach spaces |
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| Authors: | Piotr W. Nowak |
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| Affiliation: | Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland -- and -- Department of Mathematics, Tulane University, 6823 St. Charles Avenue, New Orleans, Louisiana 70118 |
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| Abstract: | ![]()
There are several characterizations of coarse embeddability of locally finite metric spaces into a Hilbert space. In this note we give such characterizations for general metric spaces. By applying these results to the spaces  , we get their coarse embeddability into a Hilbert space for  . This together with a theorem by Banach and Mazur yields that coarse embeddability into  and into  are equivalent when  . A theorem by G.Yu and the above allow us to extend to  ,  , the range of spaces, coarse embeddings into which is guaranteed for a finitely generated group  to satisfy the Novikov Conjecture. |
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| Keywords: | Coarse embeddings metric spaces Novikov Conjecture |
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