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The simple loop conjecture for 3-manifolds states that every 2-sidedimmersion of a closed surface into a 3-manifold is either injective onfundamental groups or admits a compression. This can be viewed as ageneralization of the Loop Theorem to immersed surfaces. We prove theconjecture in the case that the target 3-manifold admits a geometric structuremodeled on Sol.

The simple loop conjecture for 3-manifolds modeled on Sol