Non-isotopic transverse tori in Engel manifolds

Abstract

In every Engel manifold we construct an infinite family of pairwise non-isotopic 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.

arXiv comment10 pages, 2 figures; V2: Added Section 6 on formal transverse tori and their self-linking classes. Final version to appear in Rev. Mat. Iberoam