G5 Doctoral dissertation (article)
On metric relations between Lie groups (2021)

Kivioja, V. (2021). On metric relations between Lie groups [Doctoral dissertation]. Jyväskylän yliopisto. JYU Dissertations, 376. http://urn.fi/URN:ISBN:978-951-39-8629-2

JYU authors or editors

Publication details

All authors or editors: Kivioja, Ville

eISBN: 978-951-39-8629-2

Journal or series: JYU Dissertations

eISSN: 2489-9003

Publication year: 2021

Number in series: 376

Number of pages in the book: 1 verkkoaineisto (v, 21 sivua, 140 sivua useina numerointijaksoina, 5 numeroimatonta sivua)

Publisher: Jyväskylän yliopisto

Place of Publication: Jyväskylä

Publication country: Finland

Publication language: English

Persistent website address: http://urn.fi/URN:ISBN:978-951-39-8629-2

Publication open access: Openly available

Publication channel open access: Open Access channel

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.

Keywords: algebra; group theory; differential geometry; topology

Free keywords: algebra; group theory; differential geometry; topology

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2021