|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
Geometric limits of
cyclic subgroups of $\mathsf{SO}_0(1, k+1)$ and
$\mathsf{SU}(1, k+1)$
Sara Maloni and Maria Beatrice Pozzetti |
|
Algebraic & Geometric Topology 22 (2022) 1461–1495
|
Abstract |
|
We study geometric limits of convex-cocompact cyclic subgroups of the rank 1 groups and . We construct examples of sequences of subgroups of such groups that converge algebraically and whose geometric limits strictly contain the algebraic limits, thus generalizing the example first described by Jørgensen for subgroups of . We also give necessary and sufficient conditions for a subgroup of to arise as the geometric limit of a sequence of cyclic subgroups. We then discuss generalizations of such examples to sequences of representations of nonabelian free groups, and applications of our constructions in that setting. |
PDF Access Denied
We have not been able to recognize your IP address
18.97.14.87
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 40.00:
Keywords
geometric convergence, Jørgensen, parabolic, loxodromic,
rank 1 Lie groups
|
Mathematical Subject Classification
Primary: 22E40
Secondary: 20F67, 30F60, 57K32
|
References |
Publication
Received: 28 December 2020
Revised: 9 March 2021
Accepted: 5 April 2021
Published: 25 August 2022
|
Authors |
| Sara Maloni | |
| Department of Mathematics University of Virginia Charlottesville, VA United States |
|
| https://sites.google.com/view/sara-maloni | |
| Maria Beatrice Pozzetti | |
| Department of Mathematics University of Heidelberg Heidelberg Germany |
|
| http://www.mathi.uni-heidelberg.de/~pozzetti | |
