Fibred closed braids with disc-band fibre surfaces
Rampichini, Marta
Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004), p. 433-451 / Harvested from Biblioteca Digitale Italiana di Matematica
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A classical result by Stallings provides a necessary and sufficient condition to decide whether a given embedded surface S is a fibre in S3-∂⁡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 S3, 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 π1⁢S3∖SW.

Un risultato classico di Stallings fornisce una condizione necessaria e sufficiente per stabilire se una data superficie immersa senza autointersezioni in S3 è una fibra per S3-∂⁡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 S3, 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 π1⁢S3∖SW.

Publié le : 2004-06-01
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     author = {Marta Rampichini},
     title = {Fibred closed braids with disc-band fibre surfaces},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {7-A},
     year = {2004},
     pages = {433-451},
     zbl = {1150.57004},
     mrnumber = {2072946},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2004_8_7B_2_433_0}
}

Rampichini, Marta. Fibred closed braids with disc-band fibre surfaces. Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004) pp. 433-451. http://gdmltest.u-ga.fr/item/BUMI_2004_8_7B_2_433_0/

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