Geodesic
On the Branch Points in the Branched Coverings of Links
Canadian mathematical bulletin, Tome 28 (1985) no. 2, pp. 165-173

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DOI

Let l be a polygonal link in a 3-sphere S 3 and a branched covering of l, which depends on the choice of a monodromy map φ. Let be the link in over l. In this paper we determine the exact position of in for some cases. For instance, if l is a torus link ((n + 1)p, n) and φ is an appropriate monodromy map of the fundamental group of S3 - l into the symmetric group of degree n + 1, then is an S3 and l is a torus link (np,n 2). The 3-fold irregular branched covering of a doubled knot k is an S3, if it exists. The position of the link over k is shown in a figure. The link over knot 61 is obtained by K. A. Perko and the author, independently, and shown without proof in a paper by R. H. Fox [Can. J. Math. 22 (1970), 193-201]. The result mentioned in the above includes this case.
DOI : 10.4153/CMB-1985-017-0
Mots-clés : 57M25, 57M12 
Kinoshita, Shintchi. On the Branch Points in the Branched Coverings of Links. Canadian mathematical bulletin, Tome 28 (1985) no. 2, pp. 165-173. doi: 10.4153/CMB-1985-017-0
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     title = {On the {Branch} {Points} in the {Branched} {Coverings} of {Links}},
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     year = {1985},
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