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We give a purely geometrical smooth characterization of closed infrasolvmanifolds and orbifolds by showing that, up to diffeomorphism, these areprecisely the spaces which admit a collapse with bounded curvature and diameterto compact flat orbifolds. Moreover, we distinguish irreducible smooth faketori geometrically from standard ones by proving that the former havenon-vanishing D-minimal volume.

Seifert fiberings and collapsing of infrasolv spaces