Taut foliations, its properties and constructions
Let F be a codimension one foliation of a closed 3-manifold M.
F is called a taut foliation if all leaves of F have a closed transversal.
By the definition, F has no Reeb component.
Then a taut foliation F is Reebless and it has some properties that
the fundamental group of M is infinite,
M is irreducible and
the universal cover of M is homeomorphic to 3-dimensional Euclid space
by the theorems of Novikov, Rosenberg and Palmeira.
I will explain these properties and some example of construction of taut foliations on 3-manifolds,
especially focus on a knot complement.
If there is a time, I will explain a relation between an L-space and existence of taut foliations.