# On linking of lagrangians in symplectic 4-manifolds

## Abstract/Contents

- Abstract
- In this thesis, we study certain questions related to linking of Lagrangian submanifolds in symplectic 4-manifolds. In Chapter 2, we study linking of Lagrangian tori in R^4. Our main contribution is to prove that the linking properties of Lagrangian tori are closely connected to their enumerative geometry. As an application, we prove that any pair of monotone Clifford tori in R^4 (of possibly different monotonicity constant) are unlinked in an appropriate sense. The analogous result is false for Chekanov tori. In Chapter 3, which is joint work with Georgios Dimitroglou Rizell, we study linking of Lagrangian tori in T*T^2 and in certain rational symplectic 4-manifolds. We discuss various applications; in particular, we exhibit examples of pairs of totally real tori K_1, K_2 \subset T^2 − 0_{T^2} , each of which is isotopic to the zero section through totally real tori, but such that K_1 \cup K_2 is not smoothly isotopic to a Lagrangian. In chapter 4, which is also joint work with Georgios Dimitroglou Rizell, we study symplectic rigidity of cotangent fibers in open Riemann surfaces. This chapter can be seen as a generalization of the celebrated work of Eliashberg-Polterovich proving the Nearby Lagrangian Conjecture for T*R^2. As a corollary, we answer a strong form of a question of Eliashberg that was previously answered in dimensions at least 8 by Ekholm and Smith

## Description

Type of resource | text |
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Form | electronic resource; remote; computer; online resource |

Extent | 1 online resource |

Place | California |

Place | [Stanford, California] |

Publisher | [Stanford University] |

Copyright date | 2020; ©2020 |

Publication date | 2020; 2020 |

Issuance | monographic |

Language | English |

## Creators/Contributors

Author | Côté, Laurent Jean Barham |
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Degree supervisor | Eliashberg, Y, 1946- |

Thesis advisor | Eliashberg, Y, 1946- |

Thesis advisor | Cohen, Ralph L, 1952- |

Thesis advisor | Manolescu, Ciprian, 1978- |

Degree committee member | Cohen, Ralph L, 1952- |

Degree committee member | Manolescu, Ciprian, 1978- |

Associated with | Stanford University, Department of Mathematics. |

## Subjects

Genre | Theses |
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Genre | Text |

## Bibliographic information

Statement of responsibility | Laurent Côté |
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Note | Submitted to the Department of Mathematics |

Thesis | Thesis Ph.D. Stanford University 2020 |

Location | electronic resource |

## Access conditions

- Copyright
- © 2020 by Laurent Jean Barham Cote

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