On the extrinsic topology of Lagrangian submanifolds
By Peter Albers. 2005
53 citations recorded by the source corpus.
We investigate the extrinsic topology of Lagrangian submanifolds and of their submanifolds in closed symplectic manifolds using Floer homological methods. The first result asserts that the homology class of a displaceable monotone Lagrangian submanifold vanishes in the homology of the ambient symplectic manifold. Combining this with spectral invariants we provide a new mechanism for proving Lagrangian intersection results e.g. entailing that any two simply connected Lagrangian submanifold in $\CP^n\times\CP^n$ must intersect.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/9ccf6e1f1af5272584b623fd0041dfc6d5dfc92e
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In Applied Mathematics
- I. Smith
- O. Cornea
- P. Biran
- L. Polterovich
- Michael Entov
- R. Leclercq
- F. Zapolsky
- Francois M. Lalonde
In Geometry and Topology
Citations in the corpus
- Spectral invariants for monotone Lagrangians (2015, result): “∆) = QH∗(M) appears, for example, in [BPS03]. Various versions of Proposition 11 have appeared in the literature, see for example [EP09], as well as [BC09]; these results use early ideas appearing in [Alb05]; see also [FOOO11]. Let us point out that the estimates on spectral invariants in these pape”
- Rigidity and uniruling for Lagrangian submanifolds (2008, methodology): “Both compactification and bubbling analysis for these moduli spaces are similar to what has been discussed before to which is added the study of transversality and bubbling for the spaces of half-tubes as described by Albers in [2].”
- Floer cohomology and pencils of quadrics (2010, background): “P. Albers.”
- Cluster homology: An overview of the construction and results (2006, background): “A different proof in this case appears in [1].”
- Rigid subsets of symplectic manifolds (2007, methodology): “1(iii) below, which originated in the work by Albers [2].”
- Quantum Structures for Lagrangian Submanifolds (2007, methodology): “The map iL at point iii. is the analogue of a map first studied by Albers in [5] in the absence of bubbling.”