Classification of Engel knots
Abstract Let $$(M,{\mathcal {D}})$$ ( M ,...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2021
|
| Online Access: | https://hdl.handle.net/1721.1/131411 |
| _version_ | 1826202008578686976 |
|---|---|
| author | Casals, Roger del Pino, Álvaro |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Casals, Roger del Pino, Álvaro |
| author_sort | Casals, Roger |
| collection | MIT |
| description | Abstract
Let
$$(M,{\mathcal {D}})$$
(
M
,
D
)
be an Engel 4-manifold. We show that the scanning map from the space of Engel knots to the space of formal Engel knots is a weak homotopy equivalence when restricted to the complement of the closed
$$\ker ({\mathcal {D}})$$
ker
(
D
)
-orbits. This is a relative, parametric, and
$$C^0$$
C
0
-close h-principle. |
| first_indexed | 2024-09-23T12:00:44Z |
| format | Article |
| id | mit-1721.1/131411 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:00:44Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1314112023-02-22T17:30:32Z Classification of Engel knots Casals, Roger del Pino, Álvaro Massachusetts Institute of Technology. Department of Mathematics Abstract Let $$(M,{\mathcal {D}})$$ ( M , D ) be an Engel 4-manifold. We show that the scanning map from the space of Engel knots to the space of formal Engel knots is a weak homotopy equivalence when restricted to the complement of the closed $$\ker ({\mathcal {D}})$$ ker ( D ) -orbits. This is a relative, parametric, and $$C^0$$ C 0 -close h-principle. 2021-09-20T17:16:57Z 2021-09-20T17:16:57Z 2018-03-01 2020-09-24T20:46:36Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/131411 en https://doi.org/10.1007/s00208-017-1625-0 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Casals, Roger del Pino, Álvaro Classification of Engel knots |
| title | Classification of Engel knots |
| title_full | Classification of Engel knots |
| title_fullStr | Classification of Engel knots |
| title_full_unstemmed | Classification of Engel knots |
| title_short | Classification of Engel knots |
| title_sort | classification of engel knots |
| url | https://hdl.handle.net/1721.1/131411 |
| work_keys_str_mv | AT casalsroger classificationofengelknots AT delpinoalvaro classificationofengelknots |