Compact leaves in Reebless or taut foliations

TL;DR

This paper investigates the local structure of foliations near torus leaves, analyzing conditions under which they are taut, non-taut, or Reebless, through examples and the study of turbulization and spiraling phenomena.

Contribution

It provides a detailed analysis of foliations near torus leaves, highlighting the roles of turbulization and spiraling in determining tautness and Reeblessness.

Findings

Characterization of foliations near torus leaves

Conditions for taut, non-taut, and Reebless foliations

Insights into turbulization and spiraling processes

Abstract

Torus leaves play a crucial role in the theory of foliations. For example non-taut foliations admit a torus leaf (see the article of Goodman). In this paper, we study all the foliations near a torus leaf, and try to understand why sometimes it is taut, or non-taut (and Reebless). We focus on some crucial examples to understand non-taut and Reebless foliations; and foliations admitting a non-separating torus leaf. It relies on the study of turbulization and spiraling, with generalizations.