Non-isotopic transverse tori in Engel manifolds

TL;DR

This paper constructs infinite families of non-isotopic transverse tori in Engel manifolds, introducing a new homological invariant to distinguish them, and extends results to Legendrian tori in even contact 4-manifolds.

Contribution

It introduces a homological invariant for transverse tori in Engel manifolds and demonstrates the existence of infinitely many non-isotopic transverse tori.

Findings

Infinite families of non-isotopic transverse tori in Engel manifolds

A new homological invariant distinguishes these tori

Extension of results to Legendrian tori in even contact 4-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.