Metric equivalences of Heintze groups and applications to classifications in low dimension
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.
Main Authors
Format
Articles
Research article
Published
2022
Series
Subjects
Publication in research information system
Publisher
Duke University Press
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202302141739Use this for linking
Review status
Peer reviewed
ISSN
0019-2082
DOI
https://doi.org/10.1215/00192082-9702295
Language
English
Published in
Illinois Journal of Mathematics
Citation
- Kivioja, V., Le Donne, E., & Nicolussi Golo, S. (2022). Metric equivalences of Heintze groups and applications to classifications in low dimension. Illinois Journal of Mathematics, 66(1), 91-121. https://doi.org/10.1215/00192082-9702295
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Funder(s)
Research Council of Finland
Research Council of Finland
Research Council of Finland
European Commission
Funding program(s)
Research costs of Academy Research Fellow, AoF
Academy Research Fellow, AoF
Academy Project, AoF
ERC Starting Grant
Akatemiatutkijan tutkimuskulut, SA
Akatemiatutkija, SA
Akatemiahanke, SA
ERC Starting Grant
Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Education and Culture Executive Agency (EACEA). Neither the European Union nor EACEA can be held responsible for them.
Additional information about funding
V. K. and E. L. D. were partially supported by the European Research Council (ERC Starting Grant 713998, GeoMeG “Geometry of Metric Groups”). E. L. D. and S. N. G. were partially supported by the Academy of Finland (Grant 288501, “Geometry of Sub-Riemannian Groups,” and Grant 322898, “Sub-Riemannian Geometry via Metric-Geometry and Lie-Group Theory”). S. N. G. has been supported by the Academy of Finland (Grant 314172, “Quantitative Rectifiability in Euclidean and Non-Euclidean Spaces,” and Grant 328846, “Singular Integrals, Harmonic Functions, and Boundary Regularity in Heisenberg Groups”). V. K. was also supported by the Emil Aaltonen Foundation.
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