In every Engel manifold, we construct an infinite family of pairwise nonisotopic transverse tori that are all smoothly isotopic. To distinguish the transverse tori in the family, we introduce a homological invariant of transverse tori that is similar to the self-linking number for transverse knots in contact 3-manifolds. Analogous results are presented for Legendrian tori in even contact 4-manifolds.
Cite this article
Marc Kegel, Non-isotopic transverse tori in Engel manifolds. Rev. Mat. Iberoam. 40 (2024), no. 1, pp. 43–56DOI 10.4171/RMI/1413