Lagrangian non-intersections
type: Item
instance of: scholarly article
title: Lagrangian non-intersections
zbMATH Open document ID: 1099.53054
author: Paul Biran
published in: Geometric and Functional Analysis. GAFA
publication date: 2006-08-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0412110
review text: The paper under review presents some results concerning Lagrangian submanifolds of a symplectic manifold and their intersection patterns. Its results point out two phenomena. One of the phenomena is that in certain symplectic manifold the topology of Lagrangians with small first homology is extremely restricted. It turns out that in some cases certain assumptions on \(H_{1}(L,\mathbb{Z})\) of a Lagrangian \(L\) completely determine the entire homology of \(L\). The second phenomenon belongs to the framework of Lagrangian intersections. His results show that certain symplectic manifolds \(M\) contain some kind of ``Lagrangian core'' \(\Lambda\subset{M}\) which dominates intersections in the sense that many global Lagrangians \(L\subset{M}\) must intersect \(\Lambda\), the intersection points being irremovable by symplectic diffeomorphisms.
Mathematics Subject Classification ID: 53D35
Mathematics Subject Classification ID: 53D40
zbMATH DE Number: 5045671
zbMATH Keywords: symplectic manifolds
zbMATH Keywords: Lagrangian submanifolds
zbMATH Keywords: Floer homology
reviewed by: Mircea Puta
MaRDI profile type: Publication
OpenAlex ID: W1998867026
arXiv ID: math/0412110
DOI: 10.1007/S00039-006-0560-0
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description: scientific article