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On the cyclic coverings of the knot 52

Published online by Cambridge University Press:  20 January 2009

P. Bandieri ,
A. C. Kim  and
M. Mulazzani
P. Bandieri
Affiliation:
Dipartimento di Matematica, Università di Modena, Via Campi 213/B I-41100 Modena, Italy, E-mail address: bandieri@unimo.it
A. C. Kim
Affiliation:
Department of Mathematics, Pusan National University, Pusan 609–735, Republic of Korea, E-mail address: ackim@arirang.math.pusan.ac.kr
M. Mulazzani
Affiliation:
Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato, 5 I-40127 Bologna, Italy E-mail address: mulazza@dm.unibo.it
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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.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 3 , October 1999 , pp. 575 - 587
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

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