Constructing exact Lagrangian immersions with few double points
We establish, as an application of the results from Eliashberg and Murphy (Lagrangian caps, 2013), an h-principle for exact Lagrangian immersions with transverse self-intersections and the minimal, or near-minimal number of double points. One corollary of our result is that any orientable closed 3-m...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | en_US |
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Springer-Verlag
2015
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| Online Access: | http://hdl.handle.net/1721.1/93119 https://orcid.org/0000-0002-8787-6739 |
| _version_ | 1826204051165937664 |
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| author | Ekholm, Tobias Eliashberg, Yakov Murphy, Emmy Smith, Ivan |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Ekholm, Tobias Eliashberg, Yakov Murphy, Emmy Smith, Ivan |
| author_sort | Ekholm, Tobias |
| collection | MIT |
| description | We establish, as an application of the results from Eliashberg and Murphy (Lagrangian caps, 2013), an h-principle for exact Lagrangian immersions with transverse self-intersections and the minimal, or near-minimal number of double points. One corollary of our result is that any orientable closed 3-manifold admits an exact Lagrangian immersion into standard symplectic 6-space R[6 over st] with exactly one transverse double point. Our construction also yields a Lagrangian embedding S[superscript 1] × S[superscript 2] → R[6 over st] with vanishing Maslov class. |
| first_indexed | 2024-09-23T12:48:08Z |
| format | Article |
| id | mit-1721.1/93119 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:48:08Z |
| publishDate | 2015 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/931192022-09-28T10:06:08Z Constructing exact Lagrangian immersions with few double points Ekholm, Tobias Eliashberg, Yakov Murphy, Emmy Smith, Ivan Massachusetts Institute of Technology. Department of Mathematics Murphy, Emmy We establish, as an application of the results from Eliashberg and Murphy (Lagrangian caps, 2013), an h-principle for exact Lagrangian immersions with transverse self-intersections and the minimal, or near-minimal number of double points. One corollary of our result is that any orientable closed 3-manifold admits an exact Lagrangian immersion into standard symplectic 6-space R[6 over st] with exactly one transverse double point. Our construction also yields a Lagrangian embedding S[superscript 1] × S[superscript 2] → R[6 over st] with vanishing Maslov class. National Science Foundation (U.S.) (Grant DMS-0943787) 2015-01-22T15:34:00Z 2015-01-22T15:34:00Z 2013-08 2013-03 Article http://purl.org/eprint/type/JournalArticle 1016-443X 1420-8970 http://hdl.handle.net/1721.1/93119 Ekholm, Tobias, Yakov Eliashberg, Emmy Murphy, and Ivan Smith. “Constructing Exact Lagrangian Immersions with Few Double Points.” Geometric and Functional Analysis 23, no. 6 (December 2013): 1772–1803. https://orcid.org/0000-0002-8787-6739 en_US http://dx.doi.org/10.1007/s00039-013-0243-6 Geometric and Functional Analysis Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Springer-Verlag arXiv |
| spellingShingle | Ekholm, Tobias Eliashberg, Yakov Murphy, Emmy Smith, Ivan Constructing exact Lagrangian immersions with few double points |
| title | Constructing exact Lagrangian immersions with few double points |
| title_full | Constructing exact Lagrangian immersions with few double points |
| title_fullStr | Constructing exact Lagrangian immersions with few double points |
| title_full_unstemmed | Constructing exact Lagrangian immersions with few double points |
| title_short | Constructing exact Lagrangian immersions with few double points |
| title_sort | constructing exact lagrangian immersions with few double points |
| url | http://hdl.handle.net/1721.1/93119 https://orcid.org/0000-0002-8787-6739 |
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