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**Convergence groups and Seifert fibered 3-manifolds.**
*(English)*
Zbl 0840.57005

The authors give a new proof of D. Gabai’s result, that if \(S^1\) has a fixed orientation and \(T\) denotes the set of ordered triples \((x,y,z)\) of distinct points occurring in positive order on \(S^1\), acted on by \(\text{Homeo}_+ (S^1)\) in the obvious way, and if \(\Gamma \subset \text{Homeo}_+ (S^1)\) is a discrete convergence group, then \(T/ \Gamma\) is Seifert fibred. (By work of G. Mess and P. Scott, this implies the Seifert Fibre Space Conjecture.) The proof is by means of braid theory.

Reviewer: C.Kearton (Durham)

### MSC:

57M25 | Knots and links in the \(3\)-sphere (MSC2010) |

57M60 | Group actions on manifolds and cell complexes in low dimensions |

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\textit{A. Casson} and \textit{D. Jungreis}, Invent. Math. 118, No. 3, 441--456 (1994; Zbl 0840.57005)

### References:

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[7] | [S] P. Scott: There are no fake Seifert fibre spaces with infinite ?1. Ann. Math.117, 35-70 (1983) · Zbl 0516.57006 |

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