Annulus Isotopy for General Decomposition Surfaces

Determine whether an analogue of the Annulus Isotopy Theorem holds for every decomposition surface satisfying suitable conditions.

Background

The second stage in the paper’s construction is the alignment of product annuli with the pseudo-Anosov flow. The author identifies the extension from product annuli to general decomposition surfaces as an unresolved question, because such an extension would provide the second step of a broader flow-version of the sutured decomposition sequence.