Flexible Lagrangians
2018 ◽
Vol 2020
(8)
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pp. 2408-2435
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Abstract We introduce and discuss notions of regularity and flexibility for Lagrangian manifolds with Legendrian boundary in Weinstein domains. There is a surprising abundance of flexible Lagrangians. In turn, this leads to new constructions of Legendrians submanifolds and Weinstein manifolds. For instance, many closed n-manifolds of dimension n > 2 can be realized as exact Lagrangian submanifolds of $T^{\ast }S^n$ with possibly exotic Weinstein symplectic structures. These Weinstein structures on $T^{\ast } S^n$, infinitely many of which are distinct, are formed by a single handle attachment to the standard 2n-ball along the Legendrian boundaries of flexible Lagrangians. We also formulate a number of open problems.
2021 ◽
Vol 0
(0)
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2000 ◽
Vol 195
(2)
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pp. 371-415
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2008 ◽
Vol 4
(3)
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pp. 181-192
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2020 ◽
Vol 0
(0)
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Keyword(s):