Search results for "knot"

A potential link between serum low-density lipoproteins and asthma

2015

Finitely fibered Rosenthal compacta and trees

2009

We study some topological properties of trees with the interval topology. In particular, we characterize trees which admit a 2-fibered compactification and we present two examples of trees whose one-point compactifications are Rosenthal compact with certain renorming properties of their spaces of continuous functions.

Finite type invariants of knots in homology 3-spheres with respect to null LP-surgeries

2017

We study a theory of finite type invariants for null-homologous knots in rational homology 3-spheres with respect to null Lagrangian-preserving surgeries. It is an analogue in the setting of the rational homology of the Goussarov-Rozansky theory for knots in integral homology 3-spheres. We give a partial combinatorial description of the graded space associated with our theory and determine some cases when this description is complete. For null-homologous knots in rational homology 3-spheres with a trivial Alexander polynomial, we show that the Kricker lift of the Kontsevich integral and the Lescop equivariant invariant built from integrals in configuration spaces are universal finite type i…

On the Oort conjecture for Shimura varieties of unitary and orthogonal types

2014

In this paper we study the Oort conjecture on Shimura subvarieties contained generically in the Torelli locus in the Siegel modular variety $\mathcal{A}_g$. Using the poly-stability of Higgs bundles on curves and the slope inequality of Xiao on fibred surfaces, we show that a Shimura curve $C$ is not contained generically in the Torelli locus if its canonical Higgs bundles contains a unitary Higgs subbundle of rank at least $(4g+2)/5$. From this we prove that a Shimura subvariety of $\mathbf{SU}(n,1)$-type is not contained generically in the Torelli locus when a numerical inequality holds, which involves the genus $g$, the dimension $n+1$, the degree $2d$ of CM field of the Hermitian space,…

PERIPHERALLY SPECIFIED HOMOMORPHS OF LINK GROUPS

2005

Johnson and Livingston have characterized peripheral structures in homomorphs of knot groups. We extend their approach to the case of links. The main result is an algebraic characterization of all possible peripheral structures in certain homomorphic images of link groups.

Approximation by Certain Operators Linking the $$\alpha $$-Bernstein and the Genuine $$\alpha $$-Bernstein–Durrmeyer Operators

2020

This paper presents a new family of operators which constitute the link between \(\alpha \)-Bernstein operators and genuine \(\alpha \)-Bernstein–Durrmeyer operators. Some approximation results, which include local approximation and error estimation in terms of the modulus of continuity are given. Finally, a quantitative Voronovskaya type theorem is established and some Gruss type inequalities are obtained.

Strong Converse Results for Linking Operators and Convex Functions

2020

We consider a family B n , ρ c of operators which is a link between classical Baskakov operators (for ρ = ∞ ) and their genuine Durrmeyer type modification (for ρ = 1 ). First, we prove that for fixed n , c and a fixed convex function f , B n , ρ c f is decreasing with respect to ρ . We give two proofs, using various probabilistic considerations. Then, we combine this property with some existing direct and strong converse results for classical operators, in order to get such results for the operators B n , ρ c applied to convex functions.

Fibred-categorical obstruction theory

2022

Abstract We set up a fibred categorical theory of obstruction and classification of morphisms that specialises to the one of monoidal functors between categorical groups and also to the Schreier-Mac Lane theory of group extensions. Further applications are provided to crossed extensions and crossed bimodule butterflies, with in particular a classification of non-abelian extensions of unital associative algebras in terms of Hochschild cohomology.

Heisenberg quasiregular ellipticity

2016

Following the Euclidean results of Varopoulos and Pankka--Rajala, we provide a necessary topological condition for a sub-Riemannian 3-manifold $M$ to admit a nonconstant quasiregular mapping from the sub-Riemannian Heisenberg group $\mathbb{H}$. As an application, we show that a link complement $S^3\backslash L$ has a sub-Riemannian metric admitting such a mapping only if $L$ is empty, the unknot or Hopf link. In the converse direction, if $L$ is empty, a specific unknot or Hopf link, we construct a quasiregular mapping from $\mathbb{H}$ to $S^3\backslash L$. The main result is obtained by translating a growth condition on $\pi_1(M)$ into the existence of a supersolution to the $4$-harmonic…

Varieties of representations of virtual knot groups in SL2(C)

2002

Abstract We study the local structure of the variety of representations of a virtual knot group in SL 2 ( C ) near an abelian representation ρ 0 . To such a representation is attached a complex number ω and there are three cases. If ω and ω −1 are not roots of the Alexander polynomial, there are only abelian representations around ρ 0 . If ω is a root and ω −1 is not, there are only reducible representations. If both ω and ω −1 are roots and certain homological conditions hold, there are irreducible representations.