Fibred closed braids with disc-band fibre surfaces

Marta Rampichini

Bollettino dell'Unione Matematica Italiana (2004)

  • Volume: 7-B, Issue: 2, page 433-451
  • ISSN: 0392-4041

Abstract

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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 S 3 - ∂ ⁡ 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 π 1 ⁢ S 3 ∖ S W .

How to cite

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Rampichini, Marta. "Fibred closed braids with disc-band fibre surfaces." Bollettino dell'Unione Matematica Italiana 7-B.2 (2004): 433-451. <http://eudml.org/doc/195824>.

@article{Rampichini2004,
abstract = {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 $\pi_1 (S^\{3\} \setminus S_\{W\})$.},
author = {Rampichini, Marta},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {433-451},
publisher = {Unione Matematica Italiana},
title = {Fibred closed braids with disc-band fibre surfaces},
url = {http://eudml.org/doc/195824},
volume = {7-B},
year = {2004},
}

TY - JOUR
AU - Rampichini, Marta
TI - Fibred closed braids with disc-band fibre surfaces
JO - Bollettino dell'Unione Matematica Italiana
DA - 2004/6//
PB - Unione Matematica Italiana
VL - 7-B
IS - 2
SP - 433
EP - 451
AB - 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 $\pi_1 (S^{3} \setminus S_{W})$.
LA - eng
UR - http://eudml.org/doc/195824
ER -

References

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