5. Topological or cutandpaste constructions

Problem 5.1.
What are cutandpaste constructions of Engel structures? For example, are there branched cover or connected sum constructions? Are there localizable constructions?
Remark. There is a version of a connected sum construction in Vogelâ€™s work [vogel]. The additional assumptions made there should ideally be removed. During the workshop an open book construction due to Colin, Presas and Vogel was presented.


Problem 5.3.
If $\pi:B\rightarrow S$ is a submersion (or a Lefschetz pencil) with $B$ and $S$ compact, $B$ parallelisable, can $\ker(\pi_*)\subset TB$ be perturbed to an Engel structure?
Cite this as: AimPL: Engel structures, available at http://aimpl.org/engelstr.