Note On Coisotropic Floer Homology And Leafwise Fixed Points

Fabian Ziltener

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

For an adiscal or monotone regular coisotropic submanifold N of a symplectic manifold I define its Floer homology to be the Floer homology of a certain Lagrangian embedding of N. Given a Hamiltonian isotopy φ=(φt) and a suitable almost complex structure, the corresponding Floer chain complex is generated by the (N,φ)-contractible leafwise fixed points. I also outline the construction of a local Floer homology for an arbitrary closed coisotropic submanifold.

Results by Floer and Albers about Lagrangian Floer homology imply lower bounds on the number of leafwise fixed points. This reproduces earlier results of mine.

The first construction also gives rise to a Floer homology for a Boothby-Wang fibration, by applying it to the circle bundle inside the associated complex line bundle. This can be used to show that translated points exist.
Original languageEnglish
Pages (from-to)2553-2560
Number of pages8
JournalElectronic Research Archive
Volume29
Issue number4
DOIs
Publication statusPublished - Sept 2021

Keywords

  • Floer homology
  • coisotropic submanifold
  • leafwise fixed point
  • leafwise intersection
  • translated point

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