Given a knot K in $S^3$, it is known a standard method (by Casali and Grasselli) for constructing a 4-coloured graph representing the closed orientable 3-manifold $M=M(K,d,\omega)$ which is the d-fold covering space of $S^3$ branched over K and associated to the transitive d-representation $\omega$ of the knot group. In this paper we obtain a presentation of the fundamental group of M, directly from the Wirtinger presentation of the knot group and from the transitive d-representation $\omega$.
Fundamental groups of branched covering spaces of S^3 / Casali, Maria Rita. - In: ANNALI DELL'UNIVERSITÀ DI FERRARA. SEZIONE 7: SCIENZE MATEMATICHE. - ISSN 0430-3202. - STAMPA. - 33:(1987), pp. 247-258. [10.1007/BF02825033]
Fundamental groups of branched covering spaces of S^3
CASALI, Maria Rita
1987
Abstract
Given a knot K in $S^3$, it is known a standard method (by Casali and Grasselli) for constructing a 4-coloured graph representing the closed orientable 3-manifold $M=M(K,d,\omega)$ which is the d-fold covering space of $S^3$ branched over K and associated to the transitive d-representation $\omega$ of the knot group. In this paper we obtain a presentation of the fundamental group of M, directly from the Wirtinger presentation of the knot group and from the transitive d-representation $\omega$.
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