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On an exotic Lagrangian torus in $\mathbb{C}P^{2}$

Part of: Symplectic geometry, contact geometry

Published online by Cambridge University Press:  27 February 2015

Weiwei Wu
Weiwei Wu*
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA email wwwu@math.msu.edu
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Abstract

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We find a non-displaceable Lagrangian torus fiber in a semi-toric system which is superheavy with respect to a certain symplectic quasi-state. The proof employs both 4-dimensional techniques and those from symplectic field theory. In particular, our result implies Lagrangian $\mathbb{R}P^{2}$ is not a stem in $\mathbb{C}P^{2}$, answering a question of Entov and Polterovich.

Keywords

Lagrangian torussymplectic quasi-statesdisplaceability

MSC classification

Primary: 53D12: Lagrangian submanifolds; Maslov index 53D05: Symplectic manifolds, general
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 7 , July 2015 , pp. 1372 - 1394
Copyright
© The Author 2015 

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