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.
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48 results for “Whitehead manifold”
New 3-manifold spines with unique Whitehead graphs identified.
problem Identifying new 3-manifold spines with specific Whitehead graph types.
method Cyclic presentations and conditions on parameters to show spines of 3-manifolds.
result Examples of 3-manifolds with Whitehead graphs of specific types.
The article calculates asymptotic expansions for quantum invariants from surgeries on Whitehead link components.
problem Calculating quantum invariants for 3-manifolds resulting from surgeries on Whitehead link components.
method Asymptotic expansion of relative Reshetikhin-Turaev and Turaev-Viro invariants.
result Asymptotic formulas for both invariants are derived.
The Whitehead link complement's geometry and topology are studied using ideal triangulations and tropical geometry.
problem Understanding the geometry and topology of the Whitehead link complement and its Dehn surgeries.
method Ideal triangulations, spun-normal surfaces, and tropical geometry.
result All boundary curves of the Whitehead link complement are strongly detected by its character variety.
New examples of manifolds with similar homotopy but different simple homotopy types.
problem Characterizing groups for which high-dimensional manifolds can be homotopy equivalent but not simple homotopy equivalent.
method Construction of doubles of thickenings and use of a formula for Whitehead torsion.
result Examples of high-dimensional manifolds exist for any finitely presented group with a nontrivial Whitehead group involution.
Curious connection found between dynamical systems and 3D manifold fibrations.
problem Existence of fibrations in 3D manifolds and their relation to dynamical systems.
method Established a one-to-one correspondence between fibrations of the Whitehead link complement and `simple orbit pairs` on the torus.
result Found a correspondence between the order of rational numbers and the order of orbits in fibrations.
The Whitehead link exterior lacks most Euler class taut foliations.
problem Existence of co-orientable taut foliations with specific Euler classes.
method Combining foliation theory techniques and topological obstructions.
result Most lattice points in the dual Thurston ball cannot be Euler classes of co-orientable taut foliations.
Gabai showed that the Whitehead manifold is the union of two submanifolds each of which is homeomorphic to and whose intersection is again homeomorphic to . Using a family of generalizations of the Whitehead Link, we show that there are uncountably many contractible 3-manifolds with this doub…
Study shows bounds on knot groups and nonembeddability of certain open manifolds.
problem Nonembeddability of contractible open manifolds in compact spaces.
method Whitehead doubling and rank estimates of knot groups.
result Infinitely many non-homeomorphic contractible open manifolds cannot embed in compact spaces.
Study algebraic K-theory of 3-manifold groups using Farrell-Jones isomorphism and geometrization.
problem Algebraic K-theory of 3-manifold groups.
method Farrell-Jones isomorphism conjecture, models for virtually cyclic subgroups, geometrization theorem.
result Descriptions of Whitehead groups and algebraic K-theory groups in terms of finite subgroups and Nil-groups.
Study shows no complete positive scalar curvature for certain 3-manifolds.
problem Existence of complete metrics with positive scalar curvature on specific 3-manifolds.
method Analyzing Whitehead manifold and genus one 3-manifolds.
result No contractible genus one 3-manifold admits a complete metric of positive scalar curvature.
In this paper we study the knot Floer homology invariants of the twisted and untwisted Whitehead doubles of an arbitrary knot K. We present a formula for the filtered chain homotopy type of HFK(D(+,K,t)) in terms of the invariants for K, where D(+,K,t) denotes the t-twisted positive-clasped Whitehead double of K. In pa…
The study characterizes slopes for hyperbolic knots and Whitehead doubles.
problem Identifying characterizing slopes for hyperbolic knots and Whitehead doubles.
method Combining JSJ decompositions, geodesic lengths, and volume inequalities.
result Explicit conditions for characterizing slopes and examples of non-characterizing slopes.
Mazur's knot exterior is described by a single regular ideal octahedron, leading to hyperbolic structures related to the Whitehead link.
problem Proving nonhomeomorphism of boundaries of Mazur and Jester manifolds
method Using hyperbolic geometry, Dehn filling, and systolic geodesics
result Proving the boundaries of all Mazur and Jester manifolds are pairwise nonhomeomorphic
New examples of hyperbolic links with generalized torsion elements found.
problem Finding generalized torsion elements in the fundamental groups of hyperbolic links.
method Analyzing the Weeks manifold, figure-eight sister manifold, and Whitehead sister link to identify generalized torsion elements.
result First examples of hyperbolic links with link groups admitting generalized torsion elements.
We consider a homology sphere presented by two knots with linking number 1 and framing . We call the manifold {\it Matsumoto's manifold}. We show that there exists no contractible bound of if holds. We also give a formula of Ozsváth-Szabó's -invariant as…
The paper expands Dunwoody's classification of graphs to include all graphs satisfying the first five conditions.
problem Classifying graphs satisfying specific conditions related to Dunwoody manifolds.
method Analyzing the conditions and expanding the scope of Dunwoody's classification.
result All graphs satisfying the first five conditions are classified.
We apply a spherical CR Dehn surgery theorem in order to obtain infinitely many Dehn surgeries of the Whitehead link complement that carry spherical CR structures. We consider as starting point the spherical CR uniformization of the Whitehead link complement constructed by Parker and Will, using a Ford domain in the co…
Whitehead link surgeries are not L-spaces if they support taut foliations.
problem Characterizing rational homology spheres as L-spaces.
method Analyzing Whitehead link surgeries and their foliations.
result Whitehead link surgeries are not L-spaces if they support coorientable taut foliations.
The paper constructs infinitely many -smoothings of a -manifold.
problem Constructing -smoothings of a -manifold.
method Using controlled -cobordisms.
result Infinitely many -smoothings of a -manifold are constructed and are isotopic after taking a product with .
Defines Whitehead torsion for topological spaces via K-theory.
problem Classical Whitehead torsion for topological spaces.
method Introduces Whitehead categories and torsion cosheaves.
result Establishes a connection between Whitehead torsion and K-theory.
Study on Whitehead doubles and their sliceness properties.
problem Understanding sliceness of Whitehead doubles of knots.
method Survey of techniques to obstruct sliceness and improve bounds on non-orientable genus.
result Improved bounds on non-orientable 4 genus of Whitehead doubles and genus 1 non-orientable cobordisms to cable knots.
New obstructions show some 4-manifold homeomorphisms are pseudo-isotopic but not isotopic.
problem Tackling the difference between pseudo-isotopy and isotopy for 4-manifolds.
method Defining and showing realizable obstructions in Whitehead groups.
result Found homeomorphisms that are pseudo-isotopic but not isotopic.
Computes A-polynomials of knots from Whitehead sister link fillings.
problem Computing A-polynomials for knots from Whitehead sister link fillings.
method Using results on A-polynomials of Dehn fillings, formulas are derived for the A-polynomials of knots.
result Formulas to compute A-polynomials for knots from Whitehead sister link fillings.
Character variety of Whitehead link described in detail.
problem Character variety of Whitehead link.
method Nice description of a Zariski open subset.
result Zariski open subset of the character variety described.
Whitehead doubles have matching meridional rank and bridge number.
problem Determining the meridional rank of Whitehead doubles.
method Analyzing algebraically tame knots and their Whitehead doubles.
result Meridional rank and bridge number coincide for Whitehead doubles of prime knots.
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 volume conjecture is proven for twist knots after Dehn filling.
problem Proving the volume conjecture for twist knots after Dehn filling.
method Constructing a new ideal triangulation of the Whitehead link complement.
result Chen-Yang's volume conjecture holds for sufficiently large parameters.
We study the Whitehead torsions of inertial h-cobordisms, and identify various types representing a nested sequence of subsets of the Whitehead group. A number of examples are given to show that these subsets are all different in general.
We provide an example in each rank of an ageometric fully irreducible outer automorphism whose ideal Whitehead graph has a cut vertex. Consequently, we show that there exist examples in each rank of Handel-Mosher axis bundles that are not just a single axis, as well as of "nongeneric" behavior in the sense of the "trai…
Using geodesic currents, we provide a theoretical justification for some of the experimental results regarding the behavior of Whitehead's algorithm on non-minimal inputs, that were obtained by Haralick, Miasnikov and Myasnikov via pattern recognition methods. In particular we prove that the images of "random" elements…
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…
Paper confirms Whitehead's conjecture for aspherical 2-complexes.
problem Whitehead's conjecture about aspherical 2-complexes.
method Argument on ribbon sphere-links, generalized for aspherical 2-complexes.
result Whitehead's conjecture confirmed for aspherical 2-complexes.
We show that an immersed thrice-punctured sphere in a cusped orientable hyperbolic 3-manifold is either embedded or has a single clasp in a manifold obtained by hyperbolic Dehn filling on a cusp of the Whitehead link complement.
We construct a higher Whitehead torsion map, using algebraic K-theory of spaces, and show that it satisfies the usual properties of the classical Whitehead torsion. This is used to describe a "geometric assembly map" defined on stabilized structure spaces in purely homotopy theoretic terms.
A technique to calculate the colored Jones polynomials of satellite knots, illustrated by the Whitehead doubles of knots, is presented. Then we prove the volume conjecture for Whitehead doubles of a family of torus knots and show some interesting observations.
Whitehead doubling persistsmath.GT
The operation of (untwisted) Whitehead doubling trivializes the Alexander module of a knot (and consequently, all known abelian invariants), and converts knots to topologically slice ones. In this note we show that Whitehead doubling does not trivialize the rational function that equals to the 2-loop part of the Kontse…
We observe that Whitehead's lemma is an immediate consequence of Stallings folds.
New knots are found to be non-simple in Legendrian contact geometry.
problem Identifying non-simple Legendrian knots in contact geometry.
method Utilized knot Floer homology and the distinguished surgery triangle.
result Whitehead doubles of the trefoil are Legendrian non-simple.
We survey the recent results and current issues on the topological rigidity problem for closed aspherical manifolds, i.e., connected closed manifolds whose universal coverings are contractible. A number of open problems and conjectures are presented during the course of the discussion. We also review the status and app…
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…
We show that the infinite cyclic cover of the exterior of the untwisted Whitehead double of a non-trivial knot does not embed in any compact 3-manifold, answering a question of Jiang, Ni, Wang and Zhou.
This work classifies belted sum decompositions of fully augmented links.
problem Understanding belted sum decompositions of fully augmented links.
method Explicit classifications of thrice punctured spheres in FAL complements, geometric, combinatorial, and diagrammatic characterizations.
result Every FAL complement canonically decomposes into FALs which are either prime or two-fold covers of the Whitehead link.
Proves loop coproduct invariance under simple homotopy equivalences.
problem Invariance of loop coproduct under simple homotopy equivalences.
method Transformation formula involving Whitehead torsion.
result Loop coproduct is invariant under simple homotopy equivalences.
Proves a generalized Whitehead cut vertex lemma for tree groups.
problem Extending Whitehead's cut vertex lemma to tree group conjugacy classes.
method Proves a version of Whitehead's lemma for tree groups.
result Establishes a cut vertex in star graphs for tree group conjugacy classes.
Suppose is a hyperbolic 3-manifold which admits two Dehn fillings and such that contains an essential torus and contains an essential annulus. It is known that . We will show that if then is the Whitehead sister link exterior, and if then …
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…
We construct uncountably many simply connected open 3-manifolds with genus one ends homeomorphic to the Cantor set. Each constructed manifold has the property that any self homeomorphism of the manifold (which necessarily extends to a homeomorphism of the ends) fixes the ends pointwise. These manifolds are complements …