Boundary-at-infinity compactification of cyclic contact covers

Construct a boundary at infinity for the cyclic cover equipped with the pulled-back contact structures, together with additional characteristic-foliation data that yields a completion or compactification of the resulting contact manifold.

Background

The cyclic covers M\gamma carry pulled-back contact structures whose asymptotic slopes provide only partial information. The authors ask whether the missing asymptotic structure can be organized as a boundary at infinity carrying characteristic-foliation data, thereby producing a natural compactification.

References

Can one construct a boundary at infinity, endowed with some characteristic foliation extra data as a completion or compactification of $(M\gamma, \xi\gamma_\pm)$?

— On the Finiteness of Anosov flows on $3$-manifolds via Contact Geometry  (2609.03700 - Bowden et al., 3 Sep 2026) in Section 5, Outlook: Further Questions, Question “Completions of $M^\gamma$”