Related papers: Homogeneity of dynamically defined wild knots

Fix a field $K$. We show that $K$ is large if and only if some elementary extension of $K$ is the fraction field of a henselian local domain which is not a field. The proof uses a new result about the \'etale-open topology over $K$: if $K$…

Let G be any finitely generated infinite group. Denote by K(G) the FC-centre of G, i.e., the subgroup of all elements of G whose centralizers are of finite index in G. Let QI(G) denote the group of quasi-isometries of G with respect to word…

We prove two rigidity theorems on holomorphic isometries into homogeneous bounded domains. The first shows that a K\"ahler-Ricci soliton induced by the homogeneous metric of a homogeneous bounded domain is trivial, i.e. K\"ahler-Einstein.…

In an earlier work, we introduced a family of t-modified knot Floer homologies, defined by modifying the construction of knot Floer homology HFK-minus. The resulting groups were then used to define concordance homomorphisms indexed by t in…

We consider here the free two step nilpotent Lie group, provided with the homogeneous Kor\'anyi norm; we prove the $L^p$-boundedness of the maximal function corresponding to the homogeneous unit sphere, for some $p$.

Let $G$ be a compact Lie group acting isometrically on a compact Riemannian manifold $M$ with nonempty fixed point set $M^G$. We say that $M$ is fixed-point homogeneous if $G$ acts transitively on a normal sphere to some component of $M^G$.…

A homogeneous knot is a generalization of alternating knots and positive knots. We determine the Rasmussen invariant of a homogeneous knot. This is a new class of knots such that the Rasmussen invariant is explicitly described in terms of…

We show that, for any prime p, a knot K in the 3-sphere is determined by its p-fold cyclic unbranched covering. We also investigate when the m-fold cyclic unbranched covering of a knot coincides with the n-fold cyclic unbranched covering of…

Let K be a tame knot with irreducible exterior M(K) in a closed, connected, orientable 3--manifold Sigma such that pi_1(Sigma) is cyclic. If infinity is not a strict boundary slope, then the diameter of the set of strict boundary slopes of…

Let K be an algebraically closed field of characteristic zero. We say that a polynomial automorphism f : K^n -> K^n is special if the Jacobian of f is equal to 1. We show that every (n - 1)-dimensional component H of the set Fix(f) of fixed…

We prove that for arbitrary g, there is a surface K of genus g embedded in S4, which has finitely many extendable self-homeomorphisms' action on H1(K,Z), by defining a norm on H1(K,Z) and proving its additivity.

A fibration of a Riemannian manifold is fiberwise homogeneous if there are isometries of the manifold onto itself, taking any given fiber to any other one, and preserving fibers. Examples are fibrations of Euclidean n-space by parallel…

Let X be a noetherian scheme of finite Krull dimension, having 2 invertible in its ring of regular functions, an ample family of line bundles, and a global bound on the virtual mod-2 cohomological dimensions of its residue fields. We prove…

Any knot group is the image of the group of a prime knot by a homomorphism that preserves peripheral structure. In fact, there are infinitely many such prime knots. A related partial order on knots is defined, and its properties are…

We show that if the fundamental group of the complement of a rationally homologically fibered knot in a rational homology 3-sphere is bi-orderable, then its Alexander polynomial has at least one positive real root. Our argument can be…

Ozsv\'ath and Szab\'o used the knot filtration on $\widehat{CF}(S^3)$ to define the $\tau$-invariant for knots in the 3-sphere. In this article, we generalize their construction and define a collection of $\tau$-invariants associated to a…

Let M be a closed simply connected n-manifold of positive sectional curvature. We determine its homeomorphism or homotopic type if M also admits an isometric elementary p-group action of large rank. Our main results are: There exists a…

The conormal Lagrangian $L_K$ of a knot $K$ in $\mathbb{R}^3$ is the submanifold of the cotangent bundle $T^* \mathbb{R}^3$ consisting of covectors along $K$ that annihilate tangent vectors to $K$. By intersecting with the unit cotangent…

Let $K\leq H$ be two finite groups and let $C\leq A$ be two finite abelian groups, with $H$ acting on $A$ as a group of isomorphisms admitting $C$ as a $K$-invariant subgroup. We study the homogeneous space $X\coloneqq\left(H\ltimes…

In this paper we prove that isoperimetric sets in three-dimensional homogeneous spaces diffeomorphic to $\mathbb{R}^3$ are topological balls. We also prove that in three-dimensional homogeneous spheres isopermetric sets are either…