3-manifold groups are virtually residually p / Matthias Aschenbrenner, Stefan Friedl

Auteur: Aschenbrenner, Matthias (1972-) - AuteurCo-auteur: Friedl, Stefan (1973-) - AuteurType de document: MonographieCollection: Memoirs of the American Mathematical Society ; 1058Langue: anglaisPays: Etats UnisÉditeur: Providence (R.I.) : American Mathematical Society, 2013Description: 1 vol. (VII-100 p.) ; 26 cm ISBN: 9780821888018 ; br. Résumé: 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..Bibliographie: Bibliogr. p. 93-98. Index. Sujets MSC: 57M05 Manifolds and cell complexes -- Low-dimensional topology -- Fundamental group, presentations, free differential calculus
20E26 Group theory and generalizations -- Structure and classification of infinite or finite groups -- Residual properties and generalizations; residually finite groups
20F38 Group theory and generalizations -- Special aspects of infinite or finite groups -- Other groups related to topology or analysis
En-ligne: Site de l'auteur | MathSciNet
Location Call Number Status Date Due
Couloir 12348-01 / Séries AMS (Browse Shelf) Available

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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