scholarly journals KAUFFMAN–HARARY CONJECTURE HOLDS FOR MONTESINOS KNOTS

2004 ◽  
Vol 13 (04) ◽  
pp. 467-477 ◽  
Author(s):  
MARTA M. ASAEDA ◽  
JÓZEF H. PRZYTYCKI ◽  
ADAM S. SIKORA
Keyword(s):  
Double Cover ◽  
Incompressible Surfaces ◽  
Pretzel Knots ◽  
Prime Determinant ◽  
Alternating Links

The Kauffman–Harary conjecture states that for any reduced alternating diagram K of a knot with a prime determinant p, every non-trivial Fox p-coloring of K assigns different colors to its arcs. We generalize this conjecture by stating it in terms of homology of the double cover of S3. In this way we extend the scope of the conjecture to all prime alternating links of arbitrary determinants. We first prove the Kauffman–Harary conjecture for pretzel knots and then we generalize our argument to show the generalized Kauffman–Harary conjecture for all Montesinos links. Finally, we discuss on the relation between the conjecture and Menasco's work on incompressible surfaces in exteriors of alternating links.

Double cover K3 surfaces of Hirzebruch surfaces

2021 ◽  
Vol 21 (2) ◽  
pp. 221-225
Author(s):  
Taro Hayashi
Keyword(s):  
Rational Surface ◽  
K3 Surfaces ◽  
Double Cover ◽  
Double Covering ◽  
Smooth Surfaces ◽  
Branch Locus ◽  
Hirzebruch Surfaces ◽  
Double Covers

Abstract General K3 surfaces obtained as double covers of the n-th Hirzebruch surfaces with n = 0, 1, 4 are not double covers of other smooth surfaces. We give a criterion for such a K3 surface to be a double covering of another smooth rational surface based on the branch locus of double covers and fibre spaces of Hirzebruch surfaces.

scholarly journals Abelianisation of logarithmic $$\mathfrak {sl}_2$$-connections

2021 ◽  
Vol 27 (5) ◽  
Author(s):  
Nikita Nikolaev
Keyword(s):  
Double Cover ◽  
Direct Image

AbstractWe prove a functorial correspondence between a category of logarithmic $$\mathfrak {sl}_2$$ sl 2 -connections on a curve $${\mathsf {X}}$$ X with fixed generic residues and a category of abelian logarithmic connections on an appropriate spectral double cover "Equation missing". The proof is by constructing a pair of inverse functors $$\pi ^\text {ab}, \pi _\text {ab}$$ π ab , π ab , and the key is the construction of a certain canonical cocycle valued in the automorphisms of the direct image functor $$\pi _*$$ π ∗ .

scholarly journals Two algebraic deformations of a K3 surface

1981 ◽  
Vol 82 ◽  
pp. 1-26
Author(s):  
Daniel Comenetz
Keyword(s):  
Hyperelliptic Curve ◽  
Double Cover ◽  
Rational Curves ◽  
K3 Surface ◽  
Quartic Surface ◽  
Quadric Cone ◽  
Birational Model ◽  
Affine Line ◽  
Characteristic 2 ◽  
General Member

Let X be a nonsingular algebraic K3 surface carrying a nonsingular hyperelliptic curve of genus 3 and no rational curves. Our purpose is to study two algebraic deformations of X, viz. one specialization and one generalization. We assume the characteristic ≠ 2. The generalization of X is a nonsingular quartic surface Q in P3 : we wish to show in § 1 that there is an irreducible algebraic family of surfaces over the affine line, in which X is a member and in which Q is a general member. The specialization of X is a surface Y having a birational model which is a ramified double cover of a quadric cone in P3.

scholarly journals The effect of the variation of glass thickness and angle tilt on the performance of the double cover solar water collector

2021 ◽  
Vol 1034 (1) ◽  
pp. 012084
Author(s):  
Muhammad Nizar Ramadhan ◽  
Rachmat Subagyo ◽  
Muhammad Haris Sa’dillah ◽  
Andy Nugraha
Keyword(s):  
Double Cover ◽  
Solar Water ◽  
Glass Thickness ◽  
Water Collector

Incompressible surfaces in 2-bridge knot complements

1985 ◽  
Vol 79 (2) ◽  
pp. 225-246 ◽  
Author(s):  
A. Hatcher ◽  
W. Thurston
Keyword(s):  
Incompressible Surfaces ◽  
Knot Complements

DELTA-UNKNOTTING NUMBER FOR KNOTS

1998 ◽  
Vol 07 (05) ◽  
pp. 639-650 ◽  
Author(s):  
K. NAKAMURA ◽  
Y. NAKANISHI ◽  
Y. UCHIDA
Keyword(s):  
Torus Knots ◽  
Pretzel Knots ◽  
Minimum Number

The Δ-unknotting number for a knot is defined to be the minimum number of Δ-unknotting operations which deform the knot into the trivial knot. We determine the Δ-unknotting numbers for torus knots, positive pretzel knots, and positive closed 3-braids.

scholarly journals Rank one sheaves over quaternion algebras on Enriques surfaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Fabian Reede
Keyword(s):  
Quaternion Algebra ◽  
Double Cover ◽  
Complex Numbers ◽  
K3 Surface ◽  
Enriques Surface ◽  
Quaternion Algebras ◽  
Enriques Surfaces ◽  
Rank One ◽  
Torsion Free

Abstract Let X be an Enriques surface over the field of complex numbers. We prove that there exists a nontrivial quaternion algebra 𝓐 on X. Then we study the moduli scheme of torsion free 𝓐-modules of rank one. Finally we prove that this moduli scheme is an étale double cover of a Lagrangian subscheme in the corresponding moduli scheme on the associated covering K3 surface.

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