Examples of non-minimal open books with high fractional Dehn twist coefficient

TL;DR

This paper constructs examples of open books for 3-manifolds with high fractional Dehn twist coefficients, demonstrating that high twisting does not necessarily lead to maximal Euler characteristic of the pages.

Contribution

It provides explicit examples showing that high monodromy twisting does not guarantee maximal Euler characteristic among open books supporting the same contact structure.

Findings

High fractional Dehn twist coefficients do not imply maximal Euler characteristic.

Constructed examples as double branched covers of specific closed braids.

Challenges assumptions about the relationship between twisting and page complexity.

Abstract

In this short note we construct examples of open books for 3-manifolds that show that arbitrarily high twisting of the monodromy of the open book does not guarantee maximality of the Euler characteristic of the pages among the open books supporting the same contact manifold. We find our examples of open books as the double branched covers of families of closed braids studied by Malyutin and Netsvetaev.