Characterization of knot complements in the n-sphere

• Autorzy: Vo-Thanh Liem , Gerard A. Venema
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

knot; n-sphere; complement; homotopy groups of end

Kategorie tematyczne

• 57N35: Embeddings and immersions
• 57N15: Topology of E n , n -manifolds ( 4 n ∞ )
• 57Q45: Knots and links (in high dimensions)
• 57N45: Flatness and tameness

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1995
• Tom: 147
• Numer: 2
• Strony: 189-196

Daty

wydano

1995

otrzymano

1994-10-12

Twórcy

autor

Vo-Thanh Liem

• epartment of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487-0350, U.S.A.,

autor

Gerard A. Venema

• Department of Mathematics and Computer Science, Calvin College, Grand Rapids, Michigan 49546, U.S.A.,
• Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1003, U.S.A.

Bibliografia

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