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$N$-dimensional beaded necklaces and higher dimensional wild knots, invariant by a Schottky group

Authors :
Díaz, Juan Pablo
Hinojosa, Gabriela
Verjovsky, Alberto
Publication Year :
2024

Abstract

Starting with a smooth $n$-dimensional knot $K\subset\bS^{n+2}$, and a beaded $n$-dimensional necklace subordinated to $K$, we construct a wild knot with a Cantor set of wild points (\ie the knot is not locally flat in these points). The construction uses the conformal Schottky group acting on $\bS^{n+2}$, generated by inversions on the spheres which are the boundary of the``beads''. We show that if $K$ is a fibered knot then the wild knot is also fibered. We also study cyclic branched coverings along the wild knots.<br />Comment: 17 pages, 8 figures

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2410.15183
Document Type :
Working Paper