Pointwise packing dimension and topology of quotient sets

Determine whether the packing dimension of L(g) equals 2 at every point p∈L(g), and characterize whether L(g) has a special topological structure such as being a Cantor manifold.

Background

The quotient L(g) has topological dimension two, but its local stable and unstable components can be dendrites and its geometry is more complicated than that of a surface. The appendix explicitly states that the pointwise packing dimension and possible special topological structure of L(g) remain unresolved.

References

We would like also to observe that this question is still unsolved: Is $\dim_p L(g)=2$ at {\em all} points $p\in L(g)$? Does $L(g)$ have a special topological structure, such as Cantor manifold, etc.?

— Entropy and periodic points in pseudo-Anosov isotopy classes  (2610.26230 - Carrasco et al., 19 Oct 2026) in Appendix, Section “Questions {content} Comments”