3-Manifold Groups Are Virtually Residually P

Matthias Aschenbrenner, Stefan Friedl (Autoren)

Buch | Softcover

100 Seiten

2013
American Mathematical Society (Verlag)
978-0-8218-8801-8 (ISBN)

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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. This gives evidence for the conjecture (Thurston) that fundamental groups of $3$-manifolds are linear groups.

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 the authors prove a common generalisation 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.

Matthias Aschenbrenner, University of California, Los Angeles, CA, USA Stefan Friedl, University of Koln, Germany

Introduction Preliminaries Embedding theorems for $p$-Groups Residual properties of graphs of groups Proof of the main results The case of graph manifolds Bibliography Index

Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Gewicht	171 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-8218-8801-3 / 0821888013
ISBN-13	978-0-8218-8801-8 / 9780821888018
Zustand	Neuware