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The
classification of Lagrangians nearby the Whitney
immersion
Georgios Dimitroglou Rizell |
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Geometry & Topology 23 (2019) 3367–3458
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Abstract |
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The Whitney immersion is a Lagrangian sphere inside the four-dimensional symplectic vector space which has a single transverse double point of Whitney self-intersection number . This Lagrangian also arises as the Weinstein skeleton of the complement of a binodal cubic curve inside the projective plane, and the latter Weinstein manifold is thus the “standard” neighbourhood of Lagrangian immersions of this type. We classify the Lagrangians inside such a neighbourhood which are homologically essential, and which are either embedded or immersed with a single double point; they are shown to be Hamiltonian isotopic to either product tori, Chekanov tori, or rescalings of the Whitney immersion. |
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Keywords
nearby Lagrangian conjecture, Lagrangian fibration,
Clifford torus, Chekanov torus, Whitney immersion, Whitney
sphere
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Mathematical Subject Classification 2010
Primary: 53D12
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References |
Publication
Received: 5 March 2018
Revised: 23 October 2018
Accepted: 7 March 2019
Published: 30 December 2019
Proposed: Yasha Eliashberg
Seconded: Ciprian Manolescu, Leonid Polterovich
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Authors |
| Georgios Dimitroglou Rizell | |
| Department of Mathematics Uppsala University Uppsala Sweden |
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