3-Manifold Groups Are Virtually Residually P (Memoirs of the American Mathematical Society) - Softcover

Aschenbrenner, Matthias; Friedl, Stefan

Softcover

ISBN 10: 0821888013 ISBN 13: 9780821888018

Publisher: American Mathematical Society, 2013

Synopsis

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.

About this title

About the Author

Matthias Aschenbrenner, University of California, Los Angeles, CA, USA

Stefan Friedl, University of Koln, Germany

Edition details

• Publisher: American Mathematical Society
• Publication date: 2013
• ISBN 10: 0821888013
• ISBN 13: 9780821888018
• Binding: Paperback
• Language: English
• Number of pages: 100