Convergence groups and Seifert fibered 3-manifolds
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.
scientific article; zbMATH DE number 703863