Nearby Lagrangian fibers and Whitney sphere links
| العنوان: | Nearby Lagrangian fibers and Whitney sphere links |
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| المؤلفون: | Ivan Smith, Tobias Ekholm |
| المساهمون: | Apollo - University of Cambridge Repository |
| المصدر: | Compositio Mathematica. 154:685-718 |
| بيانات النشر: | Wiley, 2018. |
| سنة النشر: | 2018 |
| مصطلحات موضوعية: | Pure mathematics, Lagrangian link, Disjoint sets, 01 natural sciences, moduli space of holomorphic disks, Floer equation, Projection (mathematics), 0103 physical sciences, FOS: Mathematics, 0101 mathematics, Mathematics::Symplectic Geometry, stable homotopy groups of spheres, Mathematics, Algebra and Number Theory, Fiber (mathematics), symplectic field theory, 010102 general mathematics, Submanifold, 53D35, Pontrjagin-Thom construction, Compact space, Mathematics - Symplectic Geometry, Whitney sphere, Symplectic Geometry (math.SG), Embedding, Cotangent bundle, 010307 mathematical physics, Symplectic geometry |
| الوصف: | Let n>3, and let L be a Lagrangian embedding of an n-disk into the cotangent bundle of n-dimensional Euclidean space that agrees with the cotangent fiber over a non-zero point x outside a compact set. Assume that L is disjoint from the cotangent fiber at the origin. The projection of L to the base extends to a map of the n-sphere into the complement of the origin in Euclidean n-space . We show that this map is homotopically trivial, answering a question of Y. Eliashberg. We give a number of generalizations of this result, including homotopical constraints on embedded Lagrangian disks in the complement of another Lagrangian submanifold, and on two-component links of immersed Lagrangian spheres with one double point in 2n-dimensional space, under suitable dimension and Maslov index hypotheses. The proofs combine techniques from the authors' previous work, constructing bounding manifolds from moduli spaces of Floer-holomorphic disks, with symplectic field theory. v2: 39 pages, 2 figures. Numerous minor corrections and clarifications to take account of referees' suggestions. This version to appear in Compositio |
| وصف الملف: | application/pdf |
| تدمد: | 1570-5846 0010-437X |
| DOI: | 10.1112/s0010437x17007692 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::147d90f85bf58d8e615ccbe7e4ee211b https://doi.org/10.1112/s0010437x17007692 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....147d90f85bf58d8e615ccbe7e4ee211b |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 15705846 0010437X |
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| DOI: | 10.1112/s0010437x17007692 |