Quantitative algebraic topology and Lipschitz homotopy
We consider when it is possible to bound the Lipschitz constant a priori in a homotopy between Lipschitz maps. If one wants uniform bounds, this is essentially a finiteness condition on homotopy. This contrasts strongly...
| Publié dans: | Proceedings of the National Academy of Sciences of the United States of America. - National Academy of Sciences. - 110(2013), 48, Seite 19246-19250 |
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| Auteur principal: | |
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| Format: | Article en ligne |
| Langue: | English |
| Publié: |
2013
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| Accès à la collection: | Proceedings of the National Academy of Sciences of the United States of America |
| Sujets: | Physical sciences Mathematics Biological sciences Applied sciences |
| Résumé: | We consider when it is possible to bound the Lipschitz constant a priori in a homotopy between Lipschitz maps. If one wants uniform bounds, this is essentially a finiteness condition on homotopy. This contrasts strongly with the question of whether one can homotop the maps through Lipschitz maps. We also give an application to cobordism and discuss analogous isotopy questions. |
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| ISSN: | 10916490 |