arXiv research

We compute the A-polynomial 2-tuple of twisted Whitehead links. As applications, we determine canonical components of twisted Whitehead links and give a formula for the volume of twisted Whitehead link cone-manifolds.

Character variety of Whitehead link described in detail.

We prove the volume conjecture for an infinite family of links called Whitehead chains that generalizes both the Whitehead link and the Borromean rings.

The paper creates spherical CR structures for Whitehead link surgeries.

New invariants for link concordance defined using Whitehead doubles.

The Whitehead link complement's geometry and topology are studied using ideal triangulations and tropical geometry.

The article calculates asymptotic expansions for quantum invariants from surgeries on Whitehead link components.

Computes A-polynomials of knots from Whitehead sister link fillings.

Paper confirms Whitehead's conjecture for aspherical 2-complexes.

Study multiplicity of non-acyclic SL2-representations and L-functions of Whitehead links.

Study links using Soergel bimodules and Serre duality.

Whitehead link surgeries are not L-spaces if they support taut foliations.

In this paper we determine topologically the canonical component of the $SL_2(\mathbb{C})$ character variety of the Whitehead link complement.

Curious connection found between dynamical systems and 3D manifold fibrations.

New link types derived from old links.

Classifies tight contact structures on surgeries of the Whitehead link.

We determine lens surgeries (i.e.\ Dehn surgery yielding a lens space) along the $n$-twisted Whitehead link. To do so, we first give necessary conditions to yield a lens space from the Alexander polynomial of the link as: (1) $n=1$ (i.e. the Whitehead link), and (2) one of surgery coefficients is 1, 2 or 3. Our interes…

The Whitehead link exterior lacks most Euler class taut foliations.

We show that if K is any knot whose Ozsvath-Szabo concordance invariant tau(K) is positive, the all-positive Whitehead double of any iterated Bing double of K is topologically but not smoothly slice. We also show that the all-positive Whitehead double of any iterated Bing double of the Hopf link (e.g., the all-positive…

We consider the operation of Whitehead double on a component of a link and study the behavior of Milnor invariants under this operation. We show that this operation turns a link whose Milnor invariants of length < k are all zero into a link with vanishing Milnor invariants of length < 2k, and we provide formulas for th…

New examples of hyperbolic links with generalized torsion elements found.

New formulas link Milnor invariants to Heegaard Floer homology.

We describe a family of representations in SL(3,$\mathbb C$) of the fundamental group $π$ of the Whitehead link complement. These representations are obtained by considering pairs of regular order three elements in SL(3,$\mathbb C$) and can be seen as factorising through a quotient of $π$ defined by a certain exception…

Uncountably many contractible 3-manifolds with double 3-space property and those without are identified.

Bing-Whitehead Cantor sets were introduced by DeGryse and Osborne in dimension three and greater to produce examples of Cantor sets that were non standard (wild), but still had simply connected complement. In contrast to an earlier example of Kirkor, the construction techniques could be generalized to dimensions bigger…

Paper extends link Floer homology detection to almost braided links.

Mazur's knot exterior is described by a single regular ideal octahedron, leading to hyperbolic structures related to the Whitehead link.

The study computes trace fields and minimal polynomials for specific knots and links.

Using the recently proposed differential hierarchy (Z-expansion) technique, we obtain a general expression for the HOMFLY polynomials in two arbitrary symmetric representations of link families, including Whitehead and Borromean links. Among other things, this allows us to check and confirm the recent conjecture of arX…

New formulas compute link invariants using configuration space degrees.

The paper extends BPS invariants for framed knots and links.

Suppose $M$ is a hyperbolic 3-manifold which admits two Dehn fillings $M(r_1)$ and $M(r_2)$ such that $M(r_1)$ contains an essential torus and $M(r_2)$ contains an essential annulus. It is known that $Δ= Δ(r_1, r_2) \leq 5$. We will show that if $Δ= 5$ then $M$ is the Whitehead sister link exterior, and if $Δ= 4$ then …

This work classifies belted sum decompositions of fully augmented links.

In this paper we consider some families of links, including (-2,2m+1,2n)-pretzel links and twisted Whitehead links. We calculate the character varieties of these families, and determine the number of irreducible components of these character varieties.

New findings on $L$-spaces and taut foliations in hyperbolic links.

Researchers extend differential expansion to links using special framing.

The paper calculates the asymptotics of quantum invariants for Whitehead chains.

We determine the total Culler-Shalen seminorms for the 3-manifolds W_{p/q}:=W(p/q,-) obtained by Dehn filling with slope p/q on one boundary component of the Whitehead link exterior W when p is odd. As part of the proof, we use an explicit parametrization of the eigenvalue variety of W to find a one-variable polynomial…

In the paper `Automorphic functions for a Whitehead-complement group', [Osaka J Math 43 (2006) 63-77] Matsumoto, Nishi and Yoshida constructed automorphic functions on real 3-dimensional hyperbolic space for a Kleinian group called the Whitehead-link-complement group. For a Kleinian group (of the first kind), no automo…

This note shows that if two elements of equal trace (e.g., conjugate elements) generate an arithmetic two-bridge knot or link group, then the elements are parabolic. This includes the figure-eight knot and Whitehead link groups. Similarly, if two conjugate elements generate the trefoil knot group, then the elements are…

The paper extends techniques to create non-left-orderable manifolds from links with multiple boundary components.

The volume conjecture is proven for twist knots after Dehn filling.

Study volume conjecture for links with multiple hyperbolic pieces.

Profinite rigidity of certain 3-manifolds detected through Dehn fillings.

We consider a homology sphere $M_n(K_1,K_2)$ presented by two knots $K_1,K_2$ with linking number 1 and framing $(0,n)$. We call the manifold {\it Matsumoto's manifold}. We show that there exists no contractible bound of $M_n(T_{2,3},K_2)$ if $n<2τ(K_2)$ holds. We also give a formula of Ozsváth-Szabó's $τ$-invariant as…

Study shows arithmetic properties of specific hyperbolic Dehn fillings.

R.M. Kashaev conjectured that the asymptotic behavior of his link invariant, which equals the colored Jones polynomial evaluated at a root of unity, determines the hyperbolic volume of any hyperbolic link complement. We observe numerically that for knots $6_3$, $8_9$ and $8_{20}$ and for the Whitehead link, the colored…

A formula calculates the Euler class of foliations using dual graphs.