Hill, Richard M;
(2022)
Residual finiteness of extensions of arithmetic subgroups of $${{\,\mathrm{SU}\,}}(d,1)$$ with cusps.
Rendiconti del Circolo Matematico di Palermo Series 2
10.1007/s12215-022-00793-0.
(In press).
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Abstract
Let Γ be an arithmetic subgroup of SU(d,1) with cusps, and let XΓ be the associated locally symmetric space. In this paper we investigate the pre-image of Γ in the covering groups of SU(d,1). Let H∙!(XΓ,C) be the inner cohomology, i.e. the image in H∙(XΓ,C) of the compactly supported cohomology. We prove that if the first inner cohomology group H1!(XΓ,C) is non-zero then the pre-image of Γ in each connected cover of SU(d,1) is residually finite. At the end of the paper we give an example of an arithmetic subgroup Γ satisfying the criterion H1!(XΓ,C)≠0.
| Type: | Article |
|---|---|
| Title: | Residual finiteness of extensions of arithmetic subgroups of $${{\,\mathrm{SU}\,}}(d,1)$$ with cusps |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s12215-022-00793-0 |
| Publisher version: | https://doi.org/10.1007/s12215-022-00793-0 |
| Language: | English |
| Additional information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10156866 |
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