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Morse Functions Read chapter Read first chapter

2014 | OriginalPaper | Chapter

11. Floer Homology: Invariance

Authors : Michèle Audin, Mihai Damian

Published in: Morse Theory and Floer Homology

Publisher: Springer London

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Abstract

The object of this chapter is to show that the Floer homology does not depend on the chosen Hamiltonian and almost complex structure, provided the pair is regular in an appropriate sense.

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previous chapter From Floer to Morse
next chapter The Elliptic Regularity of the Floer Operator
Footnotes
1
Recall the convention we made concerning the notation ρ≥ρ 0, stated on p. 313, which stands for “ρ sufficiently large”.
 
2
Contrary to the case treated in Theorem 9.1.7.
 
3
We would like to update this list of references, adding especially the recent books and papers of some of the leading experts in the field [35, 71, 33, 10, 11], as well as the new results obtained by one of the authors [23, 24].
 
Literature
[10]
Biran, P., Cornea, O.: A Lagrangian quantum homology. In: New Perspectives and Challenges in Symplectic Field Theory. CRM Proc. Lecture Notes, vol. 49, pp. 1–44. Am. Math. Soc., Providence (2009)
[11]
[15]
Bourgeois, F.: A survey of contact homology. In: New Perspectives and Challenges in Symplectic Field Theory. CRM Proc. Lecture Notes, vol. 49, pp. 45–71. Am. Math. Soc., Providence (2009)
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[22]
Damian, M.: Constraints on exact Lagrangians in cotangent bundles of manifolds fibered over the circle. Comment. Math. Helv. 84, 705–746 (2009) MathSciNetCrossRefMATH
[23]
Damian, M.: Floer homology on the universal cover, Audin’s conjecture and other constraints on Lagrangian submanifolds. Comment. Math. Helv. 87, 433–462 (2012) MathSciNetCrossRefMATH
[24]
Damian, M.: On the topology of monotone Lagrangian submanifolds. Ann. Sci. Ec. Norm. Sup. (to appear)
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Eliashberg, Y., Givental, A., Hofer, H.: Introduction to symplectic field theory. Geom. Funct. Anal. (Special Volume, Part II), 560–673 (2000)
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Fukaya, K., Oh, Y.G., Ohta, H., Ono, K.: Lagrangian Intersection Floer Theory—Anomaly and Obstruction. AMS/IP Studies in Advanced Mathematics. International Press, Somerville (2009)
[34]
Fukaya, K., Seidel, P.: Floer homology, A ∞-categories and topological field theory. In: Geometry and Physics, Aarhus, 1995. Lecture Notes in Pure and Appl. Math., vol. 184, pp. 9–32. Dekker, New York (1997)
[35]
Fukaya, K., Seidel, P., Smith, I.: Exact Lagrangian submanifolds in simply-connected cotangent bundles. Invent. Math. 172, 1–27 (2008) MathSciNetCrossRefMATH
[36]
Gadbled, A.: Obstructions to the existence of monotone Lagrangian embeddings into cotangent bundles of manifolds fibered over the circle. Ann. Inst. Fourier (Grenoble) 59, 1135–1175 (2009) MathSciNetCrossRefMATH
[58]
Oancea, A.: A survey of Floer homology for manifolds with contact type boundary or symplectic homology. In: Symplectic geometry and Floer homology. A survey of the Floer homology for manifolds with contact type boundary or symplectic homology, Ensaios matemáticos, vol. 7, pp. 51–91. Sociedade Brasileira de Matemática (2004)
[59]
Oh, Y.G.: Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks. I. Commun. Pure Appl. Math. 46, 949–993 (1993) CrossRefMATH
[60]
Oh, Y.G.: Floer cohomology, spectral sequences and the Maslov class of Lagrangian embeddings. Int. Math. Res. Not. 7, 305–346 (1996) CrossRef
[61]
Oh, Y.G.: Symplectic topology as the geometry of action functional. I. Relative Floer theory on the cotangent bundle. J. Differ. Geom. 46, 499–577 (1997) MATH
[69]
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[71]
Seidel, P.: Fukaya Categories and Picard–Lefschetz Theory. ETH Lecture Notes Series. European Math. Soc., Zurich (2008) CrossRefMATH
[77]
Metadata
Title
Floer Homology: Invariance
Authors
Michèle Audin
Mihai Damian
Copyright Year
2014
Publisher
Springer London
Book
Morse Theory and Floer Homology

Print ISBN: 978-1-4471-5495-2

Electronic ISBN: 978-1-4471-5496-9

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-1-4471-5496-9_11

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