Contact 5-manifolds admitting open books with exotic pages

TL;DR

This paper constructs contact 5-manifolds supported by infinitely many open books with exotic Stein pages, revealing new phenomena in contact topology and Stein fillings, and describes methods to generate such examples.

Contribution

It introduces a novel construction of contact 5-manifolds with infinitely many open books having exotic Stein pages, expanding understanding of contact structures and Stein fillings.

Findings

Existence of contact 5-manifolds with infinitely many open books with exotic pages

Construction methods for generating infinitely many such examples

Distinct contact structures supported by open books with exotic Stein pages

Abstract

We construct a contact 5-manifold supported by infinitely many distinct open books with the identity monodromy and pairwise exotic Stein pages (i.e. pages are pairwise homeomorphic but non-diffeomorphic Stein fillings of a fixed contact 3-manifold), moreover we describe a process of generating infinitely many such examples. In contrast to this result, on each of $\#_{n} S^{2}\times S^{3}$ and $\#_{n} S^{2}\tilde{\times} S^{3}$ $(n\geq 2)$ we construct infinitely many open books with pairwise exotic Stein pages (and identity monodromy) supporting mutually distinct contact structures.