Geodesic
Knot manifolds with isomorphic spines
Fundamenta Mathematicae, Tome 145 (1994) no. 1, pp. 79-89

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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.
DOI : 10.4064/fm-145-1-79-89
Keywords: 3-manifold, spine, group presentation, Heegaard diagram, knot, knot group, knot manifold, peripheral system 
Alberto Cavicchioli; Friedrich Hegenbarth. Knot manifolds with isomorphic spines. Fundamenta Mathematicae, Tome 145 (1994) no. 1, pp. 79-89. doi: 10.4064/fm-145-1-79-89
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