Volume 1, issue 1 (2001)

Download this article
For printing
Recent Issues

Volume 24
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Immersed and virtually embedded $\pi_1$–injective surfaces in graph manifolds

Walter D Neumann

Algebraic & Geometric Topology 1 (2001) 411–426

arXiv: math.GT/9901085

Abstract

We show that many 3-manifold groups have no nonabelian surface subgroups. For example, any link of an isolated complex surface singularity has this property. In fact, we determine the exact class of closed graph-manifolds which have no immersed π1–injective surface of negative Euler characteristic. We also determine the class of closed graph manifolds which have no finite cover containing an embedded such surface. This is a larger class. Thus, manifolds M3 exist which have immersed π1–injective surfaces of negative Euler characteristic, but no such surface is virtually embedded (finitely covered by an embedded surface in some finite cover of M3).

Keywords
$\pi_1$-injective surface, graph manifold, separable, surface subgroup
Mathematical Subject Classification 2000
Primary: 57M10
Secondary: 57N10, 57R40, 57R42
References
Forward citations
Publication
Received: 27 March 2001
Accepted: 6 July 2001
Published: 9 July 2001
Authors
Walter D Neumann
Department of Mathematics
Barnard College
Columbia University
New York NY 10027
USA