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Obstructions to special
Lagrangian desingularizations and the Lagrangian prescribed
boundary problem
Mark Haskins and Tommaso Pacini |
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Geometry & Topology 10 (2006) 1453–1521
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arXiv: math.DG/0609352 |
Abstract |
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We exhibit infinitely many, explicit special Lagrangian isolated singularities that admit no asymptotically conical special Lagrangian smoothings. The existence/ nonexistence of such smoothings of special Lagrangian cones is an important component of the current efforts to understand which singular special Lagrangians arise as limits of smooth special Lagrangians. We also use soft methods from symplectic geometry (the relative version of the –principle for Lagrangian immersions) and tools from algebraic topology to prove (both positive and negative) results about Lagrangian desingularizations of Lagrangian submanifolds with isolated singularities; we view the (Maslov-zero) Lagrangian desingularization problem as the natural soft analogue of the special Lagrangian smoothing problem. |
Keywords
singular special Lagrangian submanifolds, smoothing,
Lagrangian h–principle, conical singularities
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Mathematical Subject Classification 2000
Primary: 53D12, 53C38
Secondary: 53C42
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References |
Forward citations |
Publication
Received: 2 July 2006
Accepted: 6 September 2006
Published: 21 October 2006
Proposed: Frances Kirwan
Seconded: Jim Bryan, Simon Donaldson
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Authors |
| Mark Haskins | |
| Department of Mathematics Imperial College London South Kensington London SW7 2AZ England |
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| Tommaso Pacini | |
| Georgia Institute of
Technology Department of Mathematics 686 Cherry Street Atlanta, GA 30332 USA |
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