Zolotov, Vladimir (2019). FINITE FLAT SPACES. Mathematika, 65 (4). S. 1010 - 1018. LONDON: LONDON MATH SOC. ISSN 2041-7942
Full text not available from this repository.Abstract
We say that a finite metric space X can be embedded almost isometrically into a class of metric spaces C if for every epsilon > 0 there exists an embedding of X into one of the elements of C with the bi-Lipschitz distortion less than 1 + epsilon. We show that almost isometric embeddability conditions are equal for the following classes of spaces. (a) Quotients of Euclidean spaces by isometric actions of finite groups. (b) L-2-Wasserstein spaces over Euclidean spaces. (c) Compact flat manifolds. (d) Compact flat orbifolds. (e) Quotients of connected compact bi-invariant Lie groups by isometric actions of compact Lie groups. (This one is the most surprising.) We call spaces which satisfy these conditions finite flat spaces. Since Markov-type constants depend only on finite subsets, we can conclude that connected compact bi-invariant Lie groups and their quotients have Markov type 2 with constant 1.
| Item Type: | Journal Article | ||||||||
| Creators: |
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| URN: | urn:nbn:de:hbz:38-160737 | ||||||||
| DOI: | 10.1112/S0025579319000263 | ||||||||
| Journal or Publication Title: | Mathematika | ||||||||
| Volume: | 65 | ||||||||
| Number: | 4 | ||||||||
| Page Range: | S. 1010 - 1018 | ||||||||
| Date: | 2019 | ||||||||
| Publisher: | LONDON MATH SOC | ||||||||
| Place of Publication: | LONDON | ||||||||
| ISSN: | 2041-7942 | ||||||||
| Language: | English | ||||||||
| Faculty: | Unspecified | ||||||||
| Divisions: | Unspecified | ||||||||
| Subjects: | no entry | ||||||||
| Uncontrolled Keywords: |
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| Refereed: | Yes | ||||||||
| URI: | http://kups.ub.uni-koeln.de/id/eprint/16073 |
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