Related papers: Some examples of dynamically defined ambient homog…

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 $p, q\in{K}$ there exists a homeomorphism $f$ of the…

In this paper we construct infinitely many wild knots, $\mathbb{S}^{n}\hookrightarrow\mathbb{S}^{n+2}$, for $n=2,3,4$ and 5, each of which is a limit set of a geometrically finite Kleinian group. We also describe some of their properties

Starting with a smooth, non-trivial $n$-dimensional knot $K\subset\bS^{n+2}$, and a beaded $n$-dimensional necklace subordinated to $K$, we construct a wild knot with a Cantor set of wild points (\ie the knot is not locally flat in these…

In this paper we study kleinian groups of Schottky type whose limit set is a wild knot in the sense of Artin and Fox. We show that, if the ``original knot'' fibers over the circle then the wild knot $\Lambda$ also fibers over the circle. As…

Let $n$ be an integer$\geqq0$. Let $S^{n+2}_1$ (respectively, $S^{n+2}_2$) be the $(n+2)$-sphere embedded in the $(n+4)$-sphere $S^{n+4}$. Let $S^{n+2}_1$ and $S^{n+2}_2$ intersect transversely. Suppose that the smooth submanifold,…

We show that the noncommutative spheres of Connes and Landi are quantum homogeneous spaces for certain compact quantum groups. We give a general construction of homogeneous spaces which support noncommutative spin geometries.

The automorphisms of free groups with boundaries form a family of groups A_{n,k} closely related to mapping class groups, with the standard automorphisms of free groups as A_{n,0} and (essentially) the symmetric automorphisms of free groups…

We present an analytical and numerical study of the Klein-Gordon kink-soliton dynamics in inhomogeneous media. In particular, we study an external field that is almost constant for the whole system but that changes its sign at the center of…

The fundamental group of the complement of a locally flat surface in a $4$-manifold is called the knot group of the surface. In this article we prove that two locally flat $2$-spheres in $\mathbb{C} P^2$ with knot group $\mathbb{Z}_2$ are…

The dynamical symmetries of the two-dimensional Klein-Gordon equations with equal scalar and vector potentials (ESVP) are studied. The dynamical symmetries are considered in the plane and the sphere respectively. The generators of the SO(3)…

In this paper, we provide explicit recursive constructions of infinitely many non-equivalent wild knots contained in the Menger sponge, in such a way that we can control their set of wild points that lies in a usual Cantor set contained in…

We give a combinatorial description of general homotopy groups of $k$-dimensional spheres with $k\geq3$ as well as those of Moore spaces. For $n>k\geq 3,$ we construct a finitely generated group defined by explicit generators and relations,…

The purpose of this paper is to construct an example of a 2-knot wildly embedded in $\mathbb{S}^{4}$ as the limit set of a Kleinian group. We find that this type of wild 2-knots has very interesting topological properties.

We consider pairs (X,Y) where X is a compact, locally CAT(-1) space, and Y is a totally geodesic subspace. The inclusion induces an embedding of the boundaries at infinity of the universal covers; we focus on the case where these are…

We present two examples of actions of non-regular locally compact quantum groups on their homogeneous spaces. The homogeneous spaces are defined in a way specific to these examples, but the definitions we use have the advantage of being…

We show that the isotropy action of a homogeneous space $G/K$, where $G$ and $K$ are compact, connected Lie groups and $K$ is defined by an automorphism on $G$, is equivariantly formal and that $(G, K)$ is a Cartan pair.

Let $n$ be any natural number. Let $K$ be any $n$-dimensional knot in $S^{n+2}$. We define a supersymmetric quantum system for $K$ with the following properties. We firstly construct a set of functional spaces (spaces of fermionic \{resp.…

The metric structure of homogeneous spaces of rank-one and rank-two associated to the real pseudo-orthogonal groups SO(p,q) and some of their contractions (e.g., ISO(p,q), Newton-Hooke type groups...) is studied. All these spaces are…

We describe relations between hyperbolic geometry and codimension two knots or, more exactly, between varieties of conjugacy classes of discrete faithful representations of the fundamental groups of hyperbolic n-manifolds M into…

Given a uniformly convergent sequence of ambient isotopies $(H_n)_{n\in\mathbb{N}}$, bijectivity of the limit function $H_\infty$ together with a minor compactness condition guarantees that $H_\infty$ is also an ambient isotopy. By…