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ISSN 1079-6762

 

Cluster homology: An overview of the construction and results


Authors: Octav Cornea and François Lalonde
Journal: Electron. Res. Announc. Amer. Math. Soc. 12 (2006), 1-12
MSC (2000): Primary 53D12; Secondary 53D40
Published electronically: February 10, 2006
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Abstract: We associate, to a Lagrangian submanifold $ L$ of a symplectic manifold, a new homology, called the cluster homology of $ L$, which is invariant up to ambient symplectic diffeomorphisms. We discuss various applications concerning analytical, topological, and dynamical properties of Lagrangian submanifolds. We also deduce a new universal Floer homology, defined without obstruction, for pairs of Lagrangian submanifolds.


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Additional Information

Octav Cornea
Affiliation: Université de Montréal, Département de Mathématiques et de Statistique, C.P. 6128 Succ. Centre-ville, Montréal H3C 3J7, Québec, Canada
Email: cornea@dms.umontreal.ca

François Lalonde
Affiliation: Université de Montréal, Département de Mathématiques et de Statistique, C.P. 6128 Succ. Centre-ville, Montréal H3C 3J7, Québec, Canada
Email: lalonde@dms.umontreal.ca

DOI: http://dx.doi.org/10.1090/S1079-6762-06-00154-5
PII: S 1079-6762(06)00154-5
Keywords: Lagrangian submanifolds, bubbling
Received by editor(s): August 31, 2005
Published electronically: February 10, 2006
Additional Notes: The authors were supported in part by individual NSERC Discovery Grants and by team FQRNT grants.
Communicated by: Leonid Polterovich
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.