Knot and braid invariants from contact homology. II.
Lie ideals and Jordan triple derivations in rings
Lifting of homeomorphisms to branched coverings of a disk
We consider a simple, possibly disconnected, d-sheeted branched covering π of a closed 2-dimensional disk D by a surface X. The isotopy classes of homeomorphisms of D which are pointwise fixed on the boundary of D and permute the branch values, form the braid group Bₙ, where n is the number of branch values. Some of these homeomorphisms can be lifted to homeomorphisms of X which fix pointwise the fiber over the base point. They form a subgroup of finite index in Bₙ. For each equivalence class...
Line Fields with Branch Defects.
Manifolds as branched covers of spheres.
Maximal actions of finite 2-groups on ℤ₂-homology 3-spheres
It is known that a finite 2-group acting on a ℤ₂-homology 3-sphere has at most ten conjugacy classes of involutions; the action of groups with the maximal number of conjugacy classes of involutions is strictly related to some questions concerning the representation of hyperbolic 3-manifolds as 2-fold branched coverings of knots. Using a low-dimensional approach we classify these maximal actions both from an algebraic and from a geometrical point of view.
Necessary Conditions for the Existence of Branched Coverings.
Nonfibered knots and representation shifts
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-standard automorphisms of branched coverings of a disk and a sphere
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 pointwise. If Y is a disk, we describe explicitly a small set of automorphisms of...
On 4-fold covering moves.
On branched coverings of 3-manifolds which fiber over the circle.
On polynomial coverings and their classification.
On Regular Homotopy of Branched Coverings of the Sphere.
On the embedding of coverings into 1-dimensional bundles.
On the Hantzsche-Wendt Manifold.
On the Homology of Metacyclic Coverings.
On the Hurwitz existence problem.
On universal groups and three-manifolds.
Open 3-manifolds and branched coverings: a quick exposition.
Open 3-manifolds, wild subsets of S3 and branched coverings.
In this paper, a representation of closed 3-manifolds as branched coverings of the 3-sphere, proved in [13], and showing a relationship between open 3-manifolds and wild knots and arcs will be illustrated by examples. It will be shown that there exist a 3-fold simple covering p : S3 --> S3 branched over the remarkable simple closed curve of Fox [4] (a wild knot). Moves are defined such that when applied to a branching set, the corresponding covering manifold remains unchanged, while the branching...