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Displaying similar documents to “Cyclic branched coverings of 2-bridge knots.”

Cyclic branched coverings of knots and homology spheres.

Francisco González-Acuña, Hamish Short (1991)

Revista Matemática de la Universidad Complutense de Madrid

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We study cyclic coverings of S3 branched over a knot, and study conditions under which the covering is a homology sphere. We show that the sequence of orders of the first homology groups for a given knot is either periodic of tends to infinity with the order of the covering, a result recently obtained independently by Riley. From our computations it follows that, if surgery on a knot k with less than 10 crossings produces a manifold with cyclic fundamental group, then k is a torus knot. ...

Nonfibered knots and representation shifts

Daniel S. Silver, Susan G. Williams (2009)

Banach Center Publications

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A conjecture of [swTAMS] states that a knot is nonfibered if and only if its infinite cyclic cover has uncountably many finite covers. We prove the conjecture for a class of knots that includes all knots of genus 1, using techniques from symbolic dynamics.

Uncountably many wild knots whose cyclic branched covering are S.

José María Montesinos-Amilibia (2003)

Revista Matemática Complutense

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There is a disk in S whose interior is PL embedded and whose boundary has a tame Cantor set of locally wild points, such that the n-fold cyclic coverings of S branched over the boundary of the disk are all S. An uncountable set of inequivalent wild knots with these properties is exhibited.