scholarly journals On branched covering representation of 4‐manifolds

2018 ◽  
Vol 100 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Riccardo Piergallini ◽  
Daniele Zuddas
Keyword(s):  
Author(s):  
Christine Breiner ◽  
Chikako Mese

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}} .


1988 ◽  
Vol 104 (1) ◽  
pp. 105-113
Author(s):  
Makoto Sakuma

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:


Author(s):  
Sanaz Golbabaei ◽  
Lawrence Roy ◽  
Prashant Kumar ◽  
Eugene Zhang

2007 ◽  
Vol 142 (2) ◽  
pp. 259-268 ◽  
Author(s):  
YUYA KODA

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.


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

2018 ◽  
Vol 27 (05) ◽  
pp. 1850030
Author(s):  
Natalia A. Viana Bedoya ◽  
Daciberg Lima Gonçalves ◽  
Elena A. Kudryavtseva

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.


2008 ◽  
Vol 17 (12) ◽  
pp. 1539-1547 ◽  
Author(s):  
LISA HERNÁNDEZ ◽  
XIAO-SONG LIN

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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