Equivariant wrapped Floer homology and symmetric periodic Reeb orbits

The aim of this article is to apply a Floer theory to study symmetric periodic Reeb orbits. We define positive equivariant wrapped Floer homology using a (anti-)symplectic involution on a Liouville domain and investigate its algebraic properties. By a careful analysis of index iterations, we obtain a non-trivial lower bound on the minimal number of geometrically distinct symmetric periodic Reeb orbits on a certain class of real contact manifolds. This includes non-degenerate real dynamically convex star-shaped hypersurfaces in R-2n which are invariant under complex conjugation. As a result, we give a partial answer to the Seifert conjecture on brake orbits in the contact setting.

Automated summary

This article applies Floer theory to study symmetric periodic Reeb orbits, defines positive equivariant wrapped Floer homology, and obtains a lower bound on the number of geometrically distinct symmetric periodic Reeb orbits on a certain class of real contact manifolds through careful analysis of index iterations.