Extension to Garcia-Sassi–Tal quotient constructions

Investigate whether methods developed for global orbit quotients in Fathi’s hyperbolic extension can be applied to the related quotient construction of García-Sassi and Tal for maps in a pseudo-Anosov isotopy class.

Background

The paper notes that García-Sassi and Tal introduced a related quotient obtained by collapsing maximal continua with bounded infinite orbits in the universal cover. That quotient lies above Fathi’s construction and is CW-expansive. The authors suggest that some of their entropy and quotient-dynamics methods may apply, but explicitly identify determining the extent of such an application as open.

References

It seems very likely that some methods in this paper can be applied in that situation; investigating such extent remains as an interesting open problem.

— Entropy and periodic points in pseudo-Anosov isotopy classes  (2610.26230 - Carrasco et al., 19 Oct 2026) in Section 1, paragraph preceding the roadmap

Does the specification property hold for all $\Phi_g$?

— Entropy and periodic points in pseudo-Anosov isotopy classes  (2610.26230 - Carrasco et al., 19 Oct 2026) in Section 6, final question