Seifert fiberings and collapsing of infrasolv spaces

2012/09/11 by Oliver Baues, Baues, Oliver, Wilderich Tuschmann +1
Mathematics · #22E25 #53C20 #55R55 #57R18 #57R55 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:22E25 #msc:53C20 #msc:55R55 #msc:57R18 #msc:57R55

paper · pdf · doi:10.48550/arxiv.1209.2450

arxiv created 2012/09/11 · openalex publication_date 2012/09/11 · arxiv updated 2012/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Metric Structures for Riemannian and Non-Riemannian Spaces

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