Seifert fiberings and collapsing of infrasolv spaces

TL;DR

This paper characterizes infrasolv manifolds and orbifolds through their collapsing behavior with bounded curvature, and distinguishes fake tori from standard ones using D-minimal volume.

Contribution

It provides a geometric smooth characterization of infrasolv spaces and differentiates fake tori based on D-minimal volume, advancing understanding of their structure.

Findings

Infrasolv manifolds admit collapse with bounded curvature to flat orbifolds.

Fake tori have non-vanishing D-minimal volume, unlike standard tori.

The paper offers a geometric criterion for identifying infrasolv spaces.

Abstract

We give a purely geometrical smooth characterization of closed infrasolv manifolds and orbifolds by showing that, up to diffeomorphism, these are precisely the spaces which admit a collapse with bounded curvature and diameter to compact flat orbifolds. Moreover, we distinguish irreducible smooth fake tori geometrically from standard ones by proving that the former have non-vanishing D-minimal volume.