Geodesic
Nonprojecting isotopies and knots with homeomorphic coverings
Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part II, Tome 66 (1976), pp. 133-147

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, new examples of nonhomeomorphic knots and links which for certain $r$ have homeomorphic $r$-sheeted cyclic branched coverings are constructed. In particular, it is proved that the two nonhomeomorphic knots with eleven crossings and with Alexander polynomial equal to one, have homeomorphic two-sheeted branched coverings, and that knots obtained from any knot by the Zeeman construction with $p$-fold and with $q$-fold twist have homeomorphic $r$-sheeted cyclic branched coverings if $p\equiv\pm q$ $(\operatorname{mod}2r)$. The construction of examples is based on regluing a link along a submanifold of codimension 1 by means of a homeomorphism which is covered by a homeomorphism which is isotopic to the identity only through nonprojecting isotopies. 
@article{ZNSL_1976_66_a3,
     author = {O. Ya. Viro},
     title = {Nonprojecting isotopies and knots with homeomorphic coverings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {133--147},
     publisher = {mathdoc},
     volume = {66},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_66_a3/}
}
TY  - JOUR
AU  - O. Ya. Viro
TI  - Nonprojecting isotopies and knots with homeomorphic coverings
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1976
SP  - 133
EP  - 147
VL  - 66
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1976_66_a3/
LA  - ru
ID  - ZNSL_1976_66_a3
ER  - 
%0 Journal Article
%A O. Ya. Viro
%T Nonprojecting isotopies and knots with homeomorphic coverings
%J Zapiski Nauchnykh Seminarov POMI
%D 1976
%P 133-147
%V 66
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_1976_66_a3/
%G ru
%F ZNSL_1976_66_a3
O. Ya. Viro. Nonprojecting isotopies and knots with homeomorphic coverings. Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part II, Tome 66 (1976), pp. 133-147. http://geodesic.mathdoc.fr/item/ZNSL_1976_66_a3/