Geodesic
Fibred closed braids with disc-band fibre surfaces
Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 2, pp. 433-451.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

A classical result by Stallings provides a necessary and sufficient condition to decide whether a given embedded surface $S$ is a fibre in $S^{3}-\partial S$. In this paper it is described how to find a candidate fibre surface for a a link presented as a closed braid. Also it is described an implemented algorithm to find the main ingredients of the necessary and sufficient condition of Stallings, namely presentations of the fundamental groups of the surface and of its complement in $S^{3}$, and an explicit expression of the homomorphism induced in homotopy by the push-off map. The paper ends with a discussion of the particular properties of the presentation of $\pi_1 (S^{3} \setminus S_{W})$.
Un risultato classico di Stallings fornisce una condizione necessaria e sufficiente per stabilire se una data superficie immersa senza autointersezioni in $S^{3}$ è una fibra per $S^{3}-\partial S$. In questo articolo si descrive come trovare una possibile fibra per un link presentato come treccia chiusa. Si descrive anche un algoritmo, implementato al calcolatore, che permette di trovare i principali ingredienti per verificare la condizione necessaria e sufficiente di Stallings, cioè una presentazione del gruppo fondamentale della superficie e del suo complementare in $S^{3}$, e una espressione esplicita dell'omomorfismo indotto in omotopia dalla mappa di push-off. L'articolo termina con una discussione di particolari proprietà della presentazione del gruppo $\pi_1 (S^{3} \setminus S_{W})$. 
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     title = {Fibred closed braids with disc-band fibre surfaces},
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Rampichini, Marta. Fibred closed braids with disc-band fibre surfaces. Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 2, pp. 433-451. http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_2_a10/

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