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Characterization of knot complements in the n-sphere

100%

Liem V.-T., Venema G. A.

Fundamenta Mathematicae

1995

tom 147

nr 2

189-196

Knot complements in the n-sphere are characterized. A connected open subset W of $S^n$ is homeomorphic with the complement of a locally flat (n-2)-sphere in $S^n$, n ≥ 4, if and only if the first homology group of W is infinite cyclic, W has one end, and the homotopy groups of the end of W are isomorphic to those of $S^1$ in dimensions less than n/2. This result generalizes earlier theorems of Daverman, Liem, and Liem and Venema.

Knot manifolds with isomorphic spines

63%

Cavicchioli A., Hegenbarth F.

Fundamenta Mathematicae

1994

tom 145

nr 1

79-89

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.

Ograniczanie wyników

2 Fundamenta Mathematicae

1 Cavicchioli A.

1 Hegenbarth F.

1 Liem V.-T.

1 Venema G. A.

1 1995

1 1994

Wyniki wyszukiwania

Characterization of knot complements in the n-sphere

Knot manifolds with isomorphic spines