Volume 16, issue 5 (2016)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The simple loop conjecture for $3$–manifolds modeled on Sol

Drew Zemke

Algebraic & Geometric Topology 16 (2016) 3051–3071
Abstract

The simple loop conjecture for 3–manifolds states that every 2–sided immersion of a closed surface into a 3–manifold is either injective on fundamental groups or admits a compression. This can be viewed as a generalization of the loop theorem to immersed surfaces. We prove the conjecture in the case that the target 3–manifold admits a geometric structure modeled on Sol.

Keywords
simple loop conjecture, Sol geometry
Mathematical Subject Classification 2010
Primary: 57M35
Secondary: 57M50
References
Publication
Received: 30 December 2015
Revised: 14 March 2016
Accepted: 28 March 2016
Published: 7 November 2016
Authors
Drew Zemke
Department of Mathematics
Cornell University
310 Malott Hall
Ithaca, NY 14853
United States
http://www.math.cornell.edu/~zemke/