Coverings of open books

TL;DR

This paper explores how open book coverings relate to virtually overtwisted contact manifolds and transverse knots, providing new examples and insights into their structure using open book foliations.

Contribution

It introduces the study of open book coverings in the context of contact topology and provides explicit examples of virtually overtwisted open books.

Findings

Open book coverings can produce transverse knots with depth greater than 1.

Explicit examples of virtually overtwisted open books are constructed.

Open book foliations are effective in analyzing these structures.

Abstract

We study a coverings of open books and virtually overtwisted contact manifolds using open book foliations. We show that open book coverings produces interesting examples such as transverse knots with depth grater than 1. We also demonstrate explicit examples of virtually overtwisted open books.