On certain Lagrangian submanifolds of S2×S2 and ℂPn
| Autor: | Joel Oakley, Michael Usher |
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| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Quadric Fiber (mathematics) Circle bundle 010102 general mathematics Torus 01 natural sciences Monotone polygon 0103 physical sciences Simply connected space Mathematics::Differential Geometry 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematics::Symplectic Geometry Hamiltonian (control theory) Symplectic geometry Mathematics |
| Zdroj: | Algebraic & Geometric Topology. 16:149-209 |
| ISSN: | 1472-2739 1472-2747 |
| Popis: | We consider various constructions of monotone Lagrangian submanifolds of ℂ Pn, S2 × S2, and quadric hypersurfaces of ℂ Pn. In S2 × S2 and ℂ P2 we show that several different known constructions of exotic monotone tori yield results that are Hamiltonian isotopic to each other, in particular answering a question of Wu by showing that the monotone fiber of a toric degeneration model of ℂ P2 is Hamiltonian isotopic to the Chekanov torus. Generalizing our constructions to higher dimensions leads us to consider monotone Lagrangian submanifolds (typically not tori) of quadrics and of ℂ Pn which can be understood either in terms of the geodesic flow on T∗Sn or in terms of the Biran circle bundle construction. Unlike previously known monotone Lagrangian submanifolds of closed simply connected symplectic manifolds, many of our higher-dimensional Lagrangian submanifolds are provably displaceable. |
| Databáze: | OpenAIRE |
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