The volume flux group and nonpositive curvature

TL;DR

This paper proves that closed nonpositively curved manifolds with non-trivial volume flux group have zero minimal volume and admit finite covers with essential circle actions, confirming a conjecture for this class.

Contribution

It establishes a link between volume flux groups, minimal volume, and circle actions on nonpositively curved manifolds, confirming a conjecture by Kedra-Kotschick-Morita.

Findings

Manifolds with non-trivial volume flux group have zero minimal volume.

Such manifolds admit finite covers with homologically essential circle actions.

The conjecture of Kedra-Kotschick-Morita is proven for this class.

Abstract

We show that every closed nonpositively curved manifold with non-trivial volume flux group has zero minimal volume, and admits a finite covering with circle actions whose orbits are homologically essential. This proves a conjecture of Kedra-Kotschick-Morita for this class of manifolds.