Determining Fuchsian groups by their finite quotients

ResearchSpace/Manakin Repository

Show simple item record

dc.contributor.author Bridson, MR en
dc.contributor.author Conder, Marston en
dc.contributor.author Reid, AW en
dc.date.accessioned 2016-10-18T04:09:54Z en
dc.date.issued 2016-07 en
dc.identifier.citation Israel Journal of Mathematics, 2016, 214(1), pp. 1-41 en
dc.identifier.issn 0021-2172 en
dc.identifier.uri http://hdl.handle.net/2292/30794 en
dc.description.abstract Let C(Γ) be the set of isomorphism classes of the finite groups that are quotients (homomorphic images) of Γ. We investigate the extent to which C(Γ) determines Γ when Γ is a group of geometric interest. If Γ1 is a lattice in PSL(2, R) and Γ2 is a lattice in any connected Lie group, then C(Γ1) = C(Γ2) implies that Γ1 ≅ Γ2. If F is a free group and Γ is a right-angled Artin group or a residually free group (with one extra condition), then C(F) = C(Γ) implies that F ≅ Γ. If Γ1 < PSL(2, C) and Γ2 < G are nonuniform arithmetic lattices, where G is a semisimple Lie group with trivial centre and no compact factors, then C(Γ1) = C(Γ2) implies that G ≅ PSL(2, C) and that Γ2 belongs to one of finitely many commensurability classes. These results are proved using the theory of profinite groups; we do not exhibit explicit finite quotients that distinguish among the groups in question. But in the special case of two non-isomorphic triangle groups, we give an explicit description of finite quotients that distinguish between them. en
dc.description.uri http://link.springer.com/journal/11856 en
dc.publisher Springer Verlag (Germany) en
dc.relation.ispartofseries Israel Journal of Mathematics en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Details obtained from http://www.sherpa.ac.uk/romeo/issn/0021-2172/ en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.subject Science & Technology en
dc.subject Physical Sciences en
dc.subject Mathematics en
dc.subject PROFINITE COMPLETIONS en
dc.subject SUBGROUP SEPARABILITY en
dc.subject SURFACE SUBGROUPS en
dc.subject ELEMENTARY THEORY en
dc.subject BIANCHI GROUPS en
dc.subject PRODUCTS en
dc.subject PROPERTY en
dc.subject GEOMETRY en
dc.title Determining Fuchsian groups by their finite quotients en
dc.type Journal Article en
dc.identifier.doi 10.1007/s11856-016-1341-6 en
pubs.issue 1 en
pubs.begin-page 1 en
pubs.volume 214 en
dc.description.version AM - Accepted Manuscript en
dc.rights.holder Copyright: Hebrew University of Jerusalem en
pubs.author-url http://link.springer.com/article/10.1007/s11856-016-1341-6 en
pubs.end-page 41 en
pubs.publication-status Published en
dc.rights.accessrights http://purl.org/eprint/accessRights/OpenAccess en
pubs.subtype Article en
pubs.elements-id 540980 en
pubs.org-id Science en
pubs.org-id Mathematics en
dc.identifier.eissn 1565-8511 en
pubs.record-created-at-source-date 2016-10-18 en


Full text options

Find Full text

This item appears in the following Collection(s)

Show simple item record

Share

Search ResearchSpace


Advanced Search

Browse