Proceedings of the Edinburgh Mathematical Society (Series 2)

Table of Contents - October 1999 - Volume 42, Issue 03  

Research Article

On the cyclic coverings of the knot 52

P. Bandieria1, A. C. Kima2 and M. Mulazzania3*

a1 Dipartimento di Matematica, Università di Modena, Via Campi 213/B I-41100 Modena, Italy, E-mail address: bandieri@unimo.it

a2 Department of Mathematics, Pusan National University, Pusan 609–735, Republic of Korea, E-mail address: ackim@arirang.math.pusan.ac.kr

a3 Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato, 5 I-40127 Bologna, Italy E-mail address: mulazza@dm.unibo.it

We construct a family of hyperbolic 3-manifolds whose fundamental groups admit a cyclic presentation. We prove that all these manifolds are cyclic branched coverings of S3 over the knot 52 and we compute their homology groups. Moreover, we show that thecyclic presentations correspond to spines of the manifolds.

(Received November 18 1997)

Footnotes

* Work partially supported by C.N.R. of Italy and by the Basic Science Research Institute Program, Korean Ministry of Education 1996, no. BSRI-96-1433. Lavoro eseguito con contributo C.N.R. & K.O.S.E.F.