On Thurston’s inequality for openbook foliations

Hiroki Kodama (ESI Junior Fellow, University of Tokyo)

Abstract: Suppose the Euler class of a Reebless codimension-1 foliation F on a closed 3-manifold is evaluated by a closed surface Σ of genus g, then its absolute value does not exceed 2g − 2. This property |⟨e(T F), [Σ]⟩| ≤ 2g − 2 is called Thurston’s inequality.

We study this inequality for openbook foliations, which have Reeb components, and introduce two families of openbook foliations. One of them satisfies the inquality and theother does not.