Frankel's conjecture on hyperbolic three-manifold groups and circle actions

A hyperbolic-like action of a group on the circle is an action by orientation-preserving circle homeomorphisms in which every non-trivial element has exactly two fixed points, one attracting and one repelling. Frankel's conjecture. Closed hyperbolic three-manifold groups do not admit hyperbolic-like actions on the circle. This conjecture concerns restrictions on circle actions of fundamental groups of closed hyperbolic three-manifolds; the supplied text does not state whether it has been resolved.

Sources & referencesView supporting material

Primary source

KyeongRo Kim and Michele Triestino, “Ping-pong dynamics of hyperbolic-like actions with non-simple points”, arXiv:2506.01690 (2025).

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