6533b82cfe1ef96bd128ebdc

RESEARCH PRODUCT

Metric equivalences of Heintze groups and applications to classifications in low dimension

Ville KiviojaEnrico Le DonneSebastiano Nicolussi Golo

subject

Mathematics - Differential GeometrydifferentiaaligeometriaDifferential Geometry (math.DG)Mathematics - Metric GeometryGeneral MathematicsFOS: MathematicsMathematics::Metric GeometryryhmäteoriaMetric Geometry (math.MG)Group Theory (math.GR)20F67 53C23 22E25 17B70 20F69 30L10 54E40Mathematics - Group Theorymetriset avaruudet

description

We approach the quasi-isometric classification questions on Lie groups by considering low dimensional cases and isometries alongside quasi-isometries. First, we present some new results related to quasi-isometries between Heintze groups. Then we will see how these results together with the existing tools related to isometries can be applied to groups of dimension 4 and 5 in particular. Thus we take steps towards determining all the equivalence classes of groups up to isometry and quasi-isometry. We completely solve the classification up to isometry for simply connected solvable groups in dimension 4, and for the subclass of groups of polynomial growth in dimension 5.

yearjournalcountryeditionlanguage
2021-04-01
http://urn.fi/URN:NBN:fi:jyu-202302141739