## Yasuharu Nakae

### 3/28(Tue)(15:40-16:40)

__Title__

**Taut foliations, its properties and constructions **

__Abstract__

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.