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
DOI:
https://doi.org/10.1090/S1079-6762-06-00154-5
Published electronically:
February 10, 2006
MathSciNet review:
2200949
Full-text PDF Free Access
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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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Bou F. Bourgeois, A Morse-Bott approach to contact homology, PhD thesis, Stanford University 2002.
CL O. Cornea, F. Lalonde, Cluster homology, arXiv:math.SG/0508345 August 2005.
FOOO K. Fukaya, Y-G. Oh, H. Ohta, K. Ono, Lagrangian intersection Floer theory—anomaly and obstruction, Preprint.
Fu K. Fukaya, Application of Floer homology of Lagrangian submanifolds to symplectic topology, To appear in the NATO-ASI 2004 volume, Kluwer, 2005.
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HoWiZe H. Hofer, K. Wysocki, E. Zehnder, Polyfolds and Fredholm theory, Preprint 2005.
McSa D. McDuff, D. Salamon, $J$-Holomorphic Curves and Symplectic Topology, AMS Colloquium Publications, Vol. 52, Providence, RI, 2004.
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Schw M. Schwarz, A quantum cup-length estimate for symplectic fixed points, Invent. Math. 133 (1998), no. 2, 353–397.
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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
MR Author ID:
346358
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
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.
