TY - JOUR
AU1 - Reni, Marco
AU2 - Zimmermann, Bruno
AB - Math. Z. 239,415–424 (2002) Digital Object Identifier (DOI) 10.1007/s002090100304 Standard situations for cyclic branched coverings of hyperbolic knots Marco Reni, Bruno Zimmermann Universita ` degli Studi di Trieste,Dipartimento di Scienze Matematiche,34100 Trieste,Italy Received: 18 February 2000; in final form: 10 October 2000 / Published online: 25 June 2001 –
 Springer-Verlag 2001 Introduction We consider the following problem: how are inequivalent knots K and K in the 3-sphere related such that the n-fold cyclic branched covering of K and the m-fold cyclic branched covering of K give the same 3-manifold M ? Let H and H denote the cyclic covering groups of K and K ,respectively. ˜ ˜ Then H fixes the preimage K of K in M,and H fixes the preimage K of K ; both preimages are simple closed curves in M . We begin by describing some standard situations which may occur (up to conjugation of the covering groups by diffeomorphisms of M ). 0.1 Standard abelian situation. The covering groups H and H of K and K commute and generate a group H ⊕H = Z ×Z of diffeomorphisms n m ˜ ˜ of M where H acts as rotations along K and H as rotations 
TI - Standard situations for cyclic branched coverings of hyperbolic knots
JF - Mathematische Zeitschrift
DO - 10.1007/s002090100304
DA - 2002-02-01
UR - https://www.deepdyve.com/lp/springer-journals/standard-situations-for-cyclic-branched-coverings-of-hyperbolic-knots-vsoelPdcZr
SP - 415
EP - 424
VL - 239
IS - 2
DP - DeepDyve
ER -