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April 2022 Metric equivalences of Heintze groups and applications to classifications in low dimension
Ville Kivioja, Enrico Le Donne, Sebastiano Nicolussi Golo
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Illinois J. Math. 66(1): 91-121 (April 2022). DOI: 10.1215/00192082-9702295

Abstract

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 toward 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.

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Ville Kivioja. Enrico Le Donne. Sebastiano Nicolussi Golo. "Metric equivalences of Heintze groups and applications to classifications in low dimension." Illinois J. Math. 66 (1) 91 - 121, April 2022. https://doi.org/10.1215/00192082-9702295

Information

Received: 24 June 2021; Revised: 12 December 2021; Published: April 2022
First available in Project Euclid: 3 February 2022

Digital Object Identifier: 10.1215/00192082-9702295

Subjects:
Primary: 20F67
Secondary: 17B70 , 20F69 , 22E25 , 30L10 , 53C23 , 54E40

Rights: Copyright © 2022 by the University of Illinois at Urbana–Champaign

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Vol.66 • No. 1 • April 2022
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