Geodesic
The simple loop conjecture for 3–manifolds modeled on Sol
Zemke, Drew1
1Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, NY 14853, United States
Algebraic and Geometric Topology, Tome 16 (2016) no. 5, pp. 3051-3071
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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.

DOI : 10.2140/agt.2016.16.3051
Classification : 57M35, 57M50
Keywords: simple loop conjecture, Sol geometry

Zemke, Drew  1

1 Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, NY 14853, United States 
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Zemke, Drew. The simple loop conjecture for 3–manifolds modeled on Sol. Algebraic and Geometric Topology, Tome 16 (2016) no. 5, pp. 3051-3071. doi: 10.2140/agt.2016.16.3051

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