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

Ville Kivioja; Enrico Le Donne; Sebastiano Nicolussi Golo

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arXiv · 2104.00368

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

Ville Kivioja·Enrico Le Donne·Sebastiano Nicolussi Golo

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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 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.

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BibTeX RIS

Ville Kivioja, Enrico Le Donne, Sebastiano Nicolussi Golo. 2021-04-01. Metric equivalences of Heintze groups and applications to classifications in low dimension. https://arxiv.org/abs/2104.00368

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