We study the relation between the concept of spine and the representation of orientable bordered 5-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 Kirby, Proc. Sympos. Pure Math. 32, Amer. Math. Soc., 1978, and Repovs, Suppl. Rend. Circ. Mat. Palermo 18 (1988), and recover the main theorem of Mitchell, Przytycki and Repovs, Bull. Polish Acad. Sci. 37 (1989) as a corollary. Finally, an application concerning knot manifolds of composite knots with h prime factors completes the paper.

Knot manifolds with isomorphic spines / Cavicchioli, Alberto; F., Hegenbarth. - In: FUNDAMENTA MATHEMATICAE. - ISSN 0016-2736. - STAMPA. - 145:(1994), pp. 79-89.

Knot manifolds with isomorphic spines

CAVICCHIOLI, Alberto;
1994

Abstract

We study the relation between the concept of spine and the representation of orientable bordered 5-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 Kirby, Proc. Sympos. Pure Math. 32, Amer. Math. Soc., 1978, and Repovs, Suppl. Rend. Circ. Mat. Palermo 18 (1988), and recover the main theorem of Mitchell, Przytycki and Repovs, Bull. Polish Acad. Sci. 37 (1989) as a corollary. Finally, an application concerning knot manifolds of composite knots with h prime factors completes the paper.
145
79
89
Knot manifolds with isomorphic spines / Cavicchioli, Alberto; F., Hegenbarth. - In: FUNDAMENTA MATHEMATICAE. - ISSN 0016-2736. - STAMPA. - 145:(1994), pp. 79-89.
Cavicchioli, Alberto; F., Hegenbarth
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/305890
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