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...
| Veröffentlicht in: | Proceedings of the National Academy of Sciences of the United States of America. - National Academy of Sciences of the United States of America. - 110(2013), 48, Seite 19246-19250 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2013
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| Zugriff auf das übergeordnete Werk: | Proceedings of the National Academy of Sciences of the United States of America |
| Schlagworte: | Physical sciences Mathematics Biological sciences Applied sciences |
| Zusammenfassung: | 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 |