A simple closed curve on the boundary of a three-manifold which is nullhomotopic in the manifold bounds a properly embedded disk. The boundary curve is retained; the Loop theorem can instead find a different simple essential curve in a nontrivial kernel.
Dehn's lemma is a result in geometric topology, specifically in the area of 3-manifolds and the study of surfaces embedded within them. It addresses how certain types of simple homotopies can be related to the topology of surfaces in 3-manifolds.
New to topics? Read the docs here!