Skip to main content
SpringerLink
Log in

The index of Floer moduli problems for parametrized action functionals

  • Original Paper
  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

We define an index for the critical points of parametrized Hamiltonian action functionals. The expected dimension of moduli spaces of parametrized Floer trajectories equals the difference of indices of the asymptotes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Albers P., Frauenfelder U.: Leaf-wise intersections and Rabinowitz Floer homology. J. Topol. Anal. 2(1), 77–98 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bourgeois, F., Oancea, A.: The Gysin exact sequence for S 1-equivariant symplectic homology (2009). arXiv:0909.4526

  3. Bourgeois F., Oancea A.: Fredholm theory and transversality for the parametrized and for the S 1-invariant symplectic action. J. Eur. Math. Soc. (JEMS) 12(5), 1181–1229 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cieliebak K., Frauenfelder U.: A Floer homology for exact contact embeddings. Pacific J. Math. 239(2), 251–316 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hutchings M.: Floer homology of families I. Algebra Geom. Topol. 8, 435–492 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kang, J.: Generalized Rabinowitz Floer homology and coisotropic intersections (2010). arXiv:1003.1009

  7. Robbin J., Salamon D.: The Maslov index for paths. Topology 32(4), 827–844 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  8. Robbin J., Salamon D.: The spectral flow and the Maslov index. Bull. Lond. Math. Soc. 27(1), 1–33 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  9. Salamon, D.: Lectures on Floer homology. In: Symplectic geometry and topology, Park City, UT, 1997; vol. 7, IAS/Park City Mathematics Series, pp. 143–229. American Mathematical Society, Providence (1999)

  10. Salamon D., Zehnder E.: Morse theory for periodic solutions of Hamiltonian systems and the Maslov index. Comm. Pure Appl. Math. 45(10), 1303–1360 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  11. Viterbo C.: Functors and computations in Floer homology with applications I. Geom. Funct. Anal. 9(5), 985–1033 (1999)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de Mathématiques CP 218, Université Libre de Bruxelles, Boulevard du Triomphe, B-1050, Bruxelles, Belgium

    Frédéric Bourgeois

  2. Institut de Recherche Mathématique Avancée, UMR 7501, CNRS, Université de Strasbourg, Strasbourg, France

    Alexandru Oancea

  3. Institute for Advanced Study, Princeton, NJ, 08540, USA

    Alexandru Oancea

Authors
  1. Frédéric Bourgeois
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexandru Oancea
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexandru Oancea.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bourgeois, F., Oancea, A. The index of Floer moduli problems for parametrized action functionals. Geom Dedicata 165, 5–24 (2013). https://doi.org/10.1007/s10711-012-9763-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10711-012-9763-8

Keywords

Mathematics Subject Classification

Search

Navigation