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Lecture: Twisted Rabinowitz-Floer Homology - Details
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General information

Course name Lecture: Twisted Rabinowitz-Floer Homology
Course number MTH-2540
Semester WS 2022/23
Current number of participants 10
Home institute Analysis und Geometrie
participating institutes Institut für Mathematik
Courses type Lecture in category Teaching
Next date Thu., 01.12.2022 14:00 - 15:30
Online/Digitale Veranstaltung Veranstaltung wird online/digital abgehalten.
Hauptunterrichtssprache englisch

Course location / Course dates

n.a. Thursday: 14:00 - 15:30, weekly
Tue., 25.10.2022 14:00 - 15:30

Comment/Description

Rabinowitz-Floer homology is the Morse-Bott homology in the sense of Floer associated with the Rabinowitz action functional introduced by Kai Cieliebak and Urs Frauenfelder in 2009. In this course, we consider a generalisation of this theory to a Rabinowitz-Floer homology of a Liouville automorphism. As an application, we show the existence of noncontractible periodic Reeb orbits on quotients of symmetric star-shaped hypersurfaces. In particular, this theory applies to lens spaces. Moreover, we prove a forcing theorem, which guarantees the existence of a contractible twisted closed characteristic on a displaceable twisted stable hypersurface in a symplectically aspherical geometrically bounded symplectic manifold if there exists a contractible twisted closed characteristic belonging to a Morse-Bott component, with energy difference smaller or equal to the displacement energy of the displaceable hypersurface.