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arXiv · 1511.04978

The simple loop conjecture for 3-manifolds modeled on Sol

Drew Zemke
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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.

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Drew Zemke. 2016-03-17. The simple loop conjecture for 3-manifolds modeled on Sol. https://doi.org/10.2140/agt.2016.16.3051

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