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$%M. R. Casali, Two-fold branched coverings of S3  have type six, Rev. Mat. Univ. Complut. Madrid 5 (1992), no. 2, 3, 235254.%$

Two-Fold Branched Coverings of S3   Have Type Six

Maria Rita CASALI
Dipartimento di Matematica
Pura et Applicata “G. Vitali”
Via Campi 213 B
Università di Modena
I-41100 Modena Italy

Received: December 13, 1991
Revised: June 12, 1992
ABSTRACT

In this work, we prove that every closed, orientable 3-manifold M3  which is a two-fold covering of  3
S  branched over a link, has type six. This implies that   3
M  is the quotient of the universal pseudocomplex K(4,6)  by the action of a finite index subgroup of a Fuchsian group with presentation

                    3   3   3   3
S(4,6)= <a1,a2,a3,a4 |a1 = a2 = a3 = a4 = a1a2a3a4 = 1>.

Moreover, the same result is proved to be true in case M3  being an unbranched covering of a two-fold branched covering of S3  .

1991 Mathematics Subject Classification: 57Q15, 57M12; 05C10, 57M25.