3-manifold groups are virtually residually p / Matthias Aschenbrenner, Stefan Friedl
Type de document : MonographieCollection : Memoirs of the American Mathematical Society, 1058Langue : anglais.Pays: Etats Unis.Éditeur : Providence (R.I.) : American Mathematical Society, 2013Description : 1 vol. (VII-100 p.) ; 26 cmISBN: 9780821888018.ISSN: 0065-9266.Bibliographie : Bibliogr. p. 93-98. Index.Sujet MSC : 57M05, Manifolds and cell complexes - General low-dimensional topology, Fundamental group, presentations, free differential calculus20E26, Structure and classification of infinite or finite groups, Residual properties and generalizations; residually finite groups
20F38, Special aspects of infinite or finite groups, Other groups related to topology or analysisEn-ligne : Site de l'auteur | MathSciNet
| Item type | Current library | Call number | Status | Date due | Barcode |
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Monographie
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CMI Salle 1 | Séries AMS (Browse shelf(Opens below)) | Available | 12348-01 |
Bibliogr. p. 93-98. Index
Given a prime p, a group is called residually p if the intersection of its p-power index normal subgroups is trivial. A group is called virtually residually p if it has a finite index subgroup which is residually p. It is well-known that finitely generated linear groups over fields of characteristic zero are virtually residually p for all but finitely many p. In particular, fundamental groups of hyperbolic 3-manifolds are virtually residually p. It is also well-known that fundamental groups of 3-manifolds are residually finite. In this paper we prove a common generalization of these results: every 3-manifold group is virtually residually p for all but finitely many p. This gives evidence for the conjecture (Thurston) that fundamental groups of 3-manifolds are linear groups.
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