# Characterization of knot complements in the n-sphere

Fundamenta Mathematicae (1995)

- Volume: 147, Issue: 2, page 189-196
- ISSN: 0016-2736

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topLiem, Vo-Thanh, and Venema, Gerard. "Characterization of knot complements in the n-sphere." Fundamenta Mathematicae 147.2 (1995): 189-196. <http://eudml.org/doc/212083>.

@article{Liem1995,

abstract = {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.},

author = {Liem, Vo-Thanh, Venema, Gerard},

journal = {Fundamenta Mathematicae},

keywords = {knot; n-sphere; complement; homotopy groups of end; knot complements; -sphere; homotopy groups of the end},

language = {eng},

number = {2},

pages = {189-196},

title = {Characterization of knot complements in the n-sphere},

url = {http://eudml.org/doc/212083},

volume = {147},

year = {1995},

}

TY - JOUR

AU - Liem, Vo-Thanh

AU - Venema, Gerard

TI - Characterization of knot complements in the n-sphere

JO - Fundamenta Mathematicae

PY - 1995

VL - 147

IS - 2

SP - 189

EP - 196

AB - 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.

LA - eng

KW - knot; n-sphere; complement; homotopy groups of end; knot complements; -sphere; homotopy groups of the end

UR - http://eudml.org/doc/212083

ER -

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