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Fibring the complement of the Fenn-Rolfsen link.

Roger Fenn (1989)

Publicacions Matemàtiques

In this note it is shown that the complement of the singular linked spheres in four dimensions defined by Fenn and Rolfsen can be fibred by tori.Also a symmetry between the two components is revealed which shows that the image provides an example of a Spanier-Whitehead duality. This provides an immediate proof that the α-invariant is non zero.

High-dimensional knots corresponding to the fractional Fibonacci groups

Andrzej Szczepański, Andreĭ Vesnin (1999)

Fundamenta Mathematicae

We prove that the natural HNN-extensions of the fractional Fibonacci groups are the fundamental groups of high-dimensional knot complements. We also give some characterization and interpretation of these knots. In particular we show that some of them are 2-knots.

Homogeneity of dynamically defined wild knots.

Gabriela Hinojosa, Alberto Verjovsky (2006)

Revista Matemática Complutense

In this paper we prove that a wild knot K which is the limit set of a Kleinian group acting conformally on the unit 3-sphere, with its standard metric, is homogeneous: given two points p, q ∈ K, there exists a homeomorphism f of the sphere such that f(K) = K and f(p) = q. We also show that if the wild knot is a fibered knot then we can choose an f which preserves the fibers.

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