Actualizing subgroups of 3-manifold groups in homologically small submanifolds

Rosemary K. Guzman, Peter B. Shalen

Let $Y$ be a simple $3$-manifold, and let $A$ be a finitely generated, freely indecomposable subgroup of $\ddot{I}{€}_1(Y)$. Set $\hat{I}\cdot =\dim H_1(A;{\mathbf{F}}_2)$. Suppose that either (a) $\partia…