The simple loop conjecture for –manifolds states that every –sided immersion of a closed surface into a –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 –manifold admits a geometric structure modeled on .
"The simple loop conjecture for $3$–manifolds modeled on Sol." Algebr. Geom. Topol. 16 (5) 3051 - 3071, 2016. https://doi.org/10.2140/agt.2016.16.3051