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

Casson, Andrew; Jungreis, Douglas

Invent. Math. 118, No. 3, 441-456 (1994).

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

Keywords:

Seifert fibred; braid; convergence group

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