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Morse Functions Read chapter Read first chapter

2014 | OriginalPaper | Chapter

14. Exercises for the Second Part

Authors : Michèle Audin, Mihai Damian

Published in: Morse Theory and Floer Homology

Publisher: Springer London

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Abstract

As its title may suggest, this chapter contains exercises on the second part (of this book).

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previous chapter The Lemmas on the Second Derivative of the Floer Operator and Other Technicalities
Footnotes
1
Even if H and K are autonomous, the composed Hamiltonian isotopy does not (in general) come from an autonomous Hamiltonian. Bonus question: When is it the case?
 
2
In [18], you can find examples of manifolds that are symplectic but not complex.
 
3
Replacing O by H and 7 by 3 would be an analogous (but more complicated) way in which to show that every oriented surface embedded in R 3 admits an almost complex structure.
 
4
For this notion, basic results, and more, see for example [5].
 
5
This means that the de Rham cohomology class of α is contained in the image of \(H^{1}(V;\mathbf{Z})\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}H^{1}(V;\mathbf{R})\).
 
Literature
[5]
Audin, M.: Torus Actions on Symplectic Manifolds. Progress in Mathematics, vol. 93, Birkhäuser, Basel (2004). Revised and enlarged edition
[8]
Berger, M., Gostiaux, B.: Géométrie différentielle: variétés, courbes et surfaces. Presses Universitaires de France (1987)
[18]
Cannas da Silva, A.: Lectures on Symplectic Geometry. Lecture Notes in Math. Springer, Berlin (2001)
Metadata
Title
Exercises for the Second Part
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_14

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