K\"unneth Formula in Rabinowitz Floer homology

TL;DR

This paper extends Rabinowitz Floer homology to certain non-contact submanifolds and proves a Künneth formula, demonstrating the existence of infinitely many leafwise intersection points.

Contribution

It introduces a Künneth formula for Rabinowitz Floer homology applicable to non-contact submanifolds, broadening the scope of the theory.

Findings

Established a Künneth formula for Rabinowitz Floer homology on non-contact submanifolds.

Proved the existence of infinitely many leafwise intersection points in the studied setting.

Extended the applicability of Rabinowitz Floer homology beyond contact type hypersurfaces.

Abstract

Rabinowitz Floer homology has been investigated on a submanifold of contact type. The contact condition, however, is quite restrictive. For example, a product of contact hypersurfaces is rarely of contact type. In this article, we study Rabinowitz Floer homology for a class of non-contact submanifolds. We show for this example that there are infinitely many leafwise intersection points by proving a K\"unneth formula for Rabinowitz Floer homology.