Periodic maximal flats are not peripheral

TL;DR

This paper proves that in certain non-positively curved symmetric spaces, all periodic maximal flats are contained within a fixed compact set, indicating they cannot be moved outside a bounded region.

Contribution

It establishes a new property of periodic maximal flats in non-positively curved locally symmetric manifolds, showing they are not peripheral.

Findings

Periodic maximal flats cannot be homotoped out of a fixed compact set.

The result applies to all non-positively curved locally symmetric manifolds of finite volume.

Abstract

We prove that every non-positively curved locally symmetric manifold M of finite volume contains a compact set K such that no periodic maximal flat can be homotoped out of K.