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Nonfibered knots and representation shifts

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

Banach Center Publications

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.

Non-slice linear combinations of algebraic knots

Matthew Hedden, Paul Kirk, Charles Livingston (2012)

Journal of the European Mathematical Society

We show that the subgroup of the knot concordance group generated by links of isolated complex singularities intersects the subgroup of algebraically slice knots in an infinite rank subgroup.

Non-standard automorphisms of branched coverings of a disk and a sphere

Bronisław Wajnryb, Agnieszka Wiśniowska-Wajnryb (2012)

Fundamenta Mathematicae

Let Y be a closed 2-dimensional disk or a 2-sphere. We consider a simple, d-sheeted branched covering π: X → Y. We fix a base point A₀ in Y (A₀ ∈ ∂Y if Y is a disk). We consider the homeomorphisms h of Y which fix ∂Y pointwise and lift to homeomorphisms ϕ of X-the automorphisms of π. We prove that if Y is a sphere then every such ϕ is isotopic by a fiber-preserving isotopy to an automorphism which fixes the fiber π - 1 ( A ) pointwise. If Y is a disk, we describe explicitly a small set of automorphisms of...

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