Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Morse Functions Read chapter Read first chapter

2014 | OriginalPaper | Chapter

7. The Geometry of the Symplectic Group, the Maslov Index

Authors : Michèle Audin, Mihai Damian

Published in: Morse Theory and Floer Homology

Publisher: Springer London

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We define a version of the Maslov index, which will play the role of the index of the critical points in the Floer complex.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter The Arnold Conjecture and the Floer Equation
next chapter Linearization and Transversality
Footnotes
1
The proof is left as an exercise for willing readers; in Exercise 43 on p. 529, we propose a proof based on Rouché’s theorem.
 
Literature
[21]
Conley, C., Zehnder, E.: Morse-type index theory for flows and periodic solutions of Hamiltonian equations. Commun. Pure Appl. Math. 37, 207–253 (1984) MathSciNetCrossRefMATH
[38]
Gelfand, I.M., Lidskii, V.B.: On the structure of the regions of stability of linear canonical systems of differential equations with periodical coefficients. Usp. Mat. Nauk 10, 3–40 (1955). Am. Math. Soc. Transl., Ser. 2 8 (1958) MathSciNet
[43]
[49]
Laudenbach, F.: Symplectic geometry and Floer homology, pp. 1–50. Sociedade Brasileira de Matemática (2004)
[50]
McDuff, D., Salamon, D.: Introduction to Symplectic Topology. Oxford Science Publications. Clarendon, New York (1995) MATH
[66]
Salamon, D.: Lectures on Floer homology. In: Eliashberg, Y., Traynor, L. (eds.) Symplectic Topology. I.A.S./Park City Math. Series. Am. Math. Soc., Providence (1999)
[67]
Salamon, D., Zehnder, E.: Morse theory for periodic solutions of Hamiltonian systems and the Maslov index. Commun. Pure Appl. Math. 45, 1003–1063 (1992) MathSciNetCrossRef
[75]
Steenrod, N.: The Topology of Fibre Bundles. Princeton University Press, Princeton (1951) MATH
Metadata
Title
The Geometry of the Symplectic Group, the Maslov Index
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_7

Premium Partner

    Image Credits