scholarly journals Spherical CR uniformization of Dehn surgeries of the Whitehead link complement

2019 ◽  
Vol 23 (5) ◽  
pp. 2593-2664 ◽  
Author(s):  
Miguel Acosta
Keyword(s):  
Whitehead Link ◽  
Link Complement

COVERING PROPERTIES OF SMALL VOLUME HYPERBOLIC 3-MANIFOLDS

1998 ◽  
Vol 07 (03) ◽  
pp. 381-392 ◽  
Author(s):  
ALEXANDER MEDNYKH ◽  
ANDREI VESNIN
Keyword(s):  
Small Volume ◽  
Whitehead Link ◽  
Covering Properties

Closed hyperbolic 3-manifolds obtained by Dehn surgeries on the Whitehead link yield interesting examples of manifolds of small volume. In the present paper these manifolds are described as 2-fold coverings of the 3-sphere branched over 3-bridge links. As a corollary, maximally symmetric [Formula: see text]-manifolds of small volume are obtained.

scholarly journals Stability properties of the colored Jones polynomial

2019 ◽  
Vol 28 (08) ◽  
pp. 1950050
Author(s):  
Christine Ruey Shan Lee
Keyword(s):  
Power Series ◽  
Jones Polynomial ◽  
Topological Information ◽  
Colored Jones Polynomial ◽  
Stability Properties ◽  
Link Complement

It is known that the colored Jones polynomial of a [Formula: see text]-adequate link has a well-defined tail consisting of stable coefficients, and that the coefficients of the tail carry geometric and topological information on the [Formula: see text]-adequate link complement. We show that a power series similar to the tail of the colored Jones polynomial for [Formula: see text]-adequate links can be defined for all links, and that it is trivial if and only if the link is non [Formula: see text]-adequate.

Surgeries on the Whitehead Link Yield Geometrically Similar Manifolds

Topology '90 ◽  
2011 ◽  
Author(s):  
Craig D. Hodgson ◽  
G. Robert Meyerhoff ◽  
Jeffrey R. Weeks
Keyword(s):  
Whitehead Link

The Generalized Cuspidal Cohomology Problem

2006 ◽  
Vol 58 (4) ◽  
pp. 673-690 ◽  
Author(s):  
Anneke Bart ◽  
Kevin P. Scannell
Keyword(s):  
Tangent Vector ◽  
Group Cohomology ◽  
Natural Generalization ◽  
Finite Range ◽  
Totally Geodesic ◽  
First Order ◽  
Link Complement ◽  
Cuspidal Cohomology ◽  
Zero Group ◽  
Geodesic Surfaces

AbstractLet Γ ⊂ SO(3, 1) be a lattice. The well known bending deformations, introduced by Thurston and Apanasov, can be used to construct non-trivial curves of representations of Γ into SO(4, 1) when Γ\ℍ3 contains an embedded totally geodesic surface. A tangent vector to such a curve is given by a non-zero group cohomology class in H1(Γ, ℍ41). Our main result generalizes this construction of cohomology to the context of “branched” totally geodesic surfaces. We also consider a natural generalization of the famous cuspidal cohomology problem for the Bianchi groups (to coefficients in non-trivial representations), and perform calculations in a finite range. These calculations lead directly to an interesting example of a link complement in S3 which is not infinitesimally rigid in SO(4, 1). The first order deformations of this link complement are supported on a piecewise totally geodesic 2-complex.

scholarly journals On SL(3, $${\varvec{\mathbb {C}}}$$ C )-representations of the Whitehead link group

2018 ◽  
Vol 202 (1) ◽  
pp. 81-101 ◽  
Author(s):  
Antonin Guilloux ◽  
Pierre Will
Keyword(s):  
Link Group ◽  
Whitehead Link

RECTANGLE CONDITION FOR COMPRESSION BODIES AND 2-FOLD BRANCHED COVERINGS

2012 ◽  
Vol 21 (08) ◽  
pp. 1250078
Author(s):  
JUNGSOO KIM ◽  
JUNG HOON LEE
Keyword(s):  
Heegaard Splitting ◽  
Level Surface ◽  
Heegaard Splittings ◽  
Branched Coverings ◽  
Link Complement ◽  
Strong Irreducibility

We give the rectangle condition for strong irreducibility of Heegaard splittings of 3-manifolds with non-empty boundary. We apply this to a generalized Heegaard splitting of 2-fold covering of S3 branched along a link. The condition implies that any thin meridional level surface in the link complement is incompressible. We also show that the additivity of width holds for a composite knot satisfying the condition.

scholarly journals CHARACTER VARIETIES OF ONCE-PUNCTURED TORUS BUNDLES WITH TUNNEL NUMBER ONE

2013 ◽  
Vol 24 (06) ◽  
pp. 1350048 ◽  
Author(s):  
KENNETH L. BAKER ◽  
KATHLEEN L. PETERSEN
Keyword(s):  
Boundary Component ◽  
Lens Space ◽  
Algebraic Sets ◽  
Character Varieties ◽  
Torus Bundles ◽  
Whitehead Link ◽  
Birational Equivalence ◽  
Punctured Torus ◽  
Tunnel Number ◽  
Trace Fields

We determine the PSL2(ℂ) and SL2(ℂ) character varieties of the once-punctured torus bundles with tunnel number one, i.e. the once-punctured torus bundles that arise from filling one boundary component of the Whitehead link exterior. In particular, we determine "natural" models for these algebraic sets, identify them up to birational equivalence with smooth models, and compute the genera of the canonical components. This enables us to compare dilatations of the monodromies of these bundles with these genera. We also determine the minimal polynomials for the trace fields of these manifolds. Additionally, we study the action of the symmetries of these manifolds upon their character varieties, identify the characters of their lens space fillings, and compute the twisted Alexander polynomials for their representations to SL2(ℂ).

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