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5. Topological or cut-and-paste constructions


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      Problem 5.1.

      What are cut-and-paste constructions of Engel structures? For example, are there branched cover or connected sum constructions? Are there localizable constructions?
        1. Remark. There is a version of a connected sum construction in Vogel’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.


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              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.