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Cluster homology: An overview of the construction and results
Author(s):
Octav
Cornea;
François
Lalonde
Journal:
Electron. Res. Announc. Amer. Math. Soc.
12
(2006),
1-12.
MSC (2000):
Primary 53D12;
Secondary 53D40
Posted:
February 10, 2006
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Abstract:
We associate, to a Lagrangian submanifold  of a symplectic manifold, a new homology, called the cluster homology of  , 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:
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
Posted:
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
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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