On Metric Relations between Lie Groups
Abstract
This thesis approaches the problem of quasi-isometric classification of Lie groups. The point of view is motivated by the known metric properties of Carnot groups, and the strategy to find similar properties in more general settings is thus twofold: First, we ask when a pair of non-isomorphic Lie groups can be made isometric using left-invariant Riemannian distances. Second, we investigate what kind of role the existence of metric dilations plays for quasi-isometry questions. Several new results and viewpoints are found, reducing metric questions to algebraic ones. Examples of the limitations of the theory and the methods to find those examples are studied.
Main Author
Format
Theses
Doctoral thesis
Published
2021
Series
ISBN
978-951-39-8629-2
Publisher
Jyväskylän yliopisto
The permanent address of the publication
https://urn.fi/URN:ISBN:978-951-39-8629-2Use this for linking
ISSN
2489-9003
Language
English
Published in
JYU Dissertations
Contains publications
- Artikkeli I: Kivioja, V., & Le Donne, E. (2017). Isometries of nilpotent metric groups. Journal de l'École polytechnique: Mathématiques, 4, 473-482. DOI: 10.5802/jep.48
- Cowling, Michael G.; Kivioja, Ville; Le Donne, Enrico; Nicolussi Golo, Sebastiano and Ottazzi, Alessandro. From homogeneous metric spaces to Lie groups. Preprint.
- Artikkeli III: Kivioja, Ville; Le Donne, Enrico and Nicolussi Golo, Sebastiano. Metric equivalences of Heintze groups and applications to classifications in low dimension. Preprint.
- Artikkeli IV: Hakavuori, Eero; Kivioja, Ville; Moisala, Terhi and Tripaldi, Francesca. Gradings for nilpotent Lie algebras. Preprint.
License
Copyright© The Author & University of Jyväskylä