scholarly journals On branched covering representation of 4‐manifolds

2018 ◽  
Vol 100 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Riccardo Piergallini ◽  
Daniele Zuddas
Keyword(s):  
Branched Covering

scholarly journals Harmonic branched coverings and uniformization of CAT(k) spheres

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Christine Breiner ◽  
Chikako Mese
Keyword(s):  
Harmonic Map ◽  
Branched Coverings ◽  
Curvature Bound ◽  
Branched Covering

Abstract Let S be a surface with a metric d satisfying an upper curvature bound in the sense of Alexandrov (i.e. via triangle comparison). We show that an almost conformal harmonic map from a surface into ( S , d ) {(S,d)} is a branched covering. As a consequence, if ( S , d ) {(S,d)} is homeomorphically equivalent to the 2-sphere 𝕊 2 {\mathbb{S}^{2}} , then it is conformally equivalent to 𝕊 2 {\mathbb{S}^{2}} .

An evaluation of the Jones polynomial of a parallel link

1988 ◽  
Vol 104 (1) ◽  
pp. 105-113
Author(s):  
Makoto Sakuma
Keyword(s):  
Jones Polynomial ◽  
Branched Covering ◽  
Parallel Link ◽  
Image Position

The Jones polynomial VL(t) of a link L in S3 contains certain information on the homology of the 2-fold branched covering D(L) of S3 branched along L. The following formulae are proved by Jones[3] and Lickorish and Millett[6] respectively:

Construction and visualization of branched covering spaces

2016 ◽  
Author(s):  
Sanaz Golbabaei ◽  
Lawrence Roy ◽  
Prashant Kumar ◽  
Eugene Zhang
Keyword(s):  
Covering Spaces ◽  
Branched Covering

Strongly-cyclic branched coverings and the Alexander polynomial of knots in rational homology spheres

2007 ◽  
Vol 142 (2) ◽  
pp. 259-268 ◽  
Author(s):  
YUYA KODA
Keyword(s):  
Fundamental Group ◽  
Homology Group ◽  
Alexander Polynomial ◽  
Homology Sphere ◽  
Cyclic Covering ◽  
Rational Homology ◽  
Branched Coverings ◽  
Branched Covering ◽  
Rational Homology Spheres ◽  
Rational Homology Sphere

AbstractLet K be a knot in a rational homology sphere M. In this paper we correlate the Alexander polynomial of K with a g-word cyclic presentation for the fundamental group of the strongly-cyclic covering of M branched over K. We also give a formula for the order of the first homology group of the strongly-cyclic branched covering.

Interactive Design and Visualization of Branched Covering Spaces

2018 ◽  
Vol 24 (1) ◽  
pp. 843-852 ◽  
Author(s):  
Lawrence Roy ◽  
Prashant Kumar ◽  
Sanaz Golbabaei ◽  
Yue Zhang ◽  
Eugene Zhang
Keyword(s):  
Interactive Design ◽  
Covering Spaces ◽  
Branched Covering

scholarly journals Indecomposable branched coverings over the projective plane by surfaces M with χ(M) ≤ 0

2018 ◽  
Vol 27 (05) ◽  
pp. 1850030
Author(s):  
Natalia A. Viana Bedoya ◽  
Daciberg Lima Gonçalves ◽  
Elena A. Kudryavtseva
Keyword(s):  
Projective Plane ◽  
Euler Characteristic ◽  
Covering Surface ◽  
Branched Coverings ◽  
Branched Covering

In this work, we study the decomposability property of branched coverings of degree [Formula: see text] odd, over the projective plane, where the covering surface has Euler characteristic [Formula: see text]. The latter condition is equivalent to say that the defect of the covering is greater than [Formula: see text]. We show that, given a datum [Formula: see text] with an even defect greater than [Formula: see text], it is realizable by an indecomposable branched covering over the projective plane. The case when [Formula: see text] is even is known.

AN APPLICATION OF TQFT: DETERMINING THE GIRTH OF A KNOT

2008 ◽  
Vol 17 (12) ◽  
pp. 1539-1547 ◽  
Author(s):  
LISA HERNÁNDEZ ◽  
XIAO-SONG LIN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Upper Bound ◽  
Topological Quantum Field Theory ◽  
Quantum Field ◽  
Heegaard Genus ◽  
Kauffman Bracket ◽  
Branched Covering ◽  
Topological Quantum ◽  
Intersection Points

A knot diagram can be divided by a circle into two parts, such that each part can be coded by a planar tree with integer weights on its edges. A half of the number of intersection points of this circle with the knot diagram is called the girth. The girth of a knot is the minimal girth of all diagrams of this knot. The girth of a knot minus one is an upper bound of the Heegaard genus of the 2-fold branched covering of that knot. We will use Topological Quantum Field Theory (TQFT) coming from the Kauffman bracket to determine the girth of some knots. Consequently, our method can be used to determine the Heegaard genus of the 2-fold branched covering of some knots.

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