SIMPLE 4-KNOTS
1998 ◽
Vol 07
(07)
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pp. 907-923
We show that the isotopy type of a 1-simple n-knot K is determined by the Postnikov (n - 1)-stage of its exterior X(K), together with the homotopy class of the longitude λK ∈ πn(X(K)). Moreover any pair (X, j) where X is a 4-dimensional homology circle with π1(X) ≅ Z and j : S4 × S1 → X is such that (X, j) = (MCyl(j), S4 × S1) is an orientable PD6-pair is realizable by some simple 4-knot. We derive complete algebraic characterizations of torsion free fibred simple 4-knots and of Artin spins of fibred simple 3-knots.
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1970 ◽
Vol 30
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pp. 32-40
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2020 ◽
Vol 27
(1)
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pp. 43-47
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2001 ◽
Vol 64
(1)
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pp. 71-79
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2011 ◽
Vol 39
(8)
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pp. 2981-3020
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