Foliations and Diffeomorphism Groups — Question 46

Definitions and mathematical statement

The supplied record asks for a characterization of pairs of prelaminations with a universal property. It does not define a prelamination, specify the admissible pairs, construct their corresponding bifoliated plane, or define an "Ansov-like" action (the spelling in the supplied question).

To display the intended quantifiers without supplying missing hypotheses, let $(L_1,L_2)$ denote a candidate pair, write $P(L_1,L_2)$ for its corresponding bifoliated plane when that correspondence is defined, and let $\mathcal A_G(L_1,L_2)$ denote the group actions of $G$ that preserve the pair in the intended sense. These symbols are placeholders for constructions and classes not specified in the record. The question is to characterize the pairs for which \[ \forall\,\text{groups }G\;\forall\alpha\in\mathcal A_G(L_1,L_2),\qquad \alpha\text{ induces an ``Ansov-like'' action of }G\text{ on }P(L_1,L_2). \] Here "induces" retains the unspecified correspondence in the source; no construction or uniqueness of the induced action is asserted. The admissible prelaminations, the meaning of preservation, the correspondence with a bifoliated plane, and the action property must be supplied before this schema becomes a precise mathematical statement. In particular, the record does not determine whether "Ansov-like" means "Anosov-like," or which definition of that term is intended.

Short English statement

Characterize pairs of prelaminations such that every group action preserving the pair induces an "Ansov-like" action on the associated bifoliated plane. The necessary definitions and correspondence are absent from the supplied record, so this is a provisional formulation requiring mathematical review.

Sources

• Supplied local UnsolvedMath registry record: permanent ID $800105$, exact source problem code catalogue entry, title "Foliations and Diffeomorphism Groups --- Question 46." The record attributes the problem to Nariman and Yazdi, with proposed year 2025.
• Nariman and Yazdi, Problem List on Foliations and Diffeomorphism Groups (2025), Question 46. Supplied source URL: https://arxiv.org/abs/2503.18274. This is the authoritative-source reference supplied by the registry; its contents have not been independently consulted for this draft.
• Supplied provenance: access date 2026-10-16; extraction method arxiv_latex; upstream revision d371ee917ac9647fbb06cd6fc529deec6f3dda82. The access date records supplied provenance, not access performed for this draft. The registry labels the problem "open"; that label is supplied metadata, not an independently verified literature assessment.