We study the relation between the concept of spine and the representation of orientable bordered 3-manifolds by Heegaard diagrams. As a consequence, we show that composing invertible non-amphicheiral knots yields examples of topologically different knot manifolds with isomorphic spines. These results are related to some questions listed in [9], [11] and recover the main theorem of [10] as a corollary. Finally, an application concerning knot manifolds of composite knots with h prime factors completes the paper.
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This is a survey of results and open problems on compact 3-manifolds which admit spines corresponding to cyclic presentations of groups. We also discuss questions concerning spines of knot manifolds and regular neighborhoods of homotopically PL embedded compacta in 3-manifolds.
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