Contact open books with exotic pages

TL;DR

The paper constructs infinitely many contact 5-manifolds from a fixed contact 3-manifold with exotic Stein fillings, showing these 5-manifolds are all diffeomorphic but have distinct contact structures, and explicitly classifies them.

Contribution

It demonstrates a method to produce infinitely many non-contactomorphic contact 5-manifolds from a single contact 3-manifold with exotic Stein fillings, explicitly classifying these manifolds.

Findings

All constructed contact 5-manifolds are diffeomorphic.

The contact 5-manifolds are pairwise non-contactomorphic.

Explicit classification of the resulting contact 5-manifolds.

Abstract

We consider a fixed contact 3-manifold that admits infinitely many compact Stein fillings which are all homeomorphic but pairwise non-diffeomorphic. Each of these fillings gives rise to a closed contact 5-manifold described as a contact open book whose page is the filling at hand and whose monodromy is the identity symplectomorphism. We show that the resulting infinitely many contact 5-manifolds are all diffeomorphic but pairwise non-contactomorphic. Moreover, we explicitly determine these contact 5-manifolds.