Quasigeodesic flows and Möbius-like groups

Abstract

If M is a hyperbolic 3-manifold with a quasigeodesic flow then we show that π_1(M) acts in a natural way on a closed disc by homeomorphisms. Consequently, such a flow either has a closed orbit or the action on the boundary circle is Möbius-like but not conjugate into PSL(2, R). We conjecture that the latter possibility cannot occur.

22 pages, 5 figures

References in corpus (1)

• Ideal boundaries of pseudo-Anosov flows and uniform convergence groups, with connections and applications to large scale geometry