# Morse structures on partial open books with extendable monodromy

## TL;DR

This paper extends Morse structures from open books to partial open books with extendable monodromy, providing a new framework to study contact 3-manifolds with convex boundary.

## Contribution

It introduces Morse structures on partial open books with extendable monodromy, broadening the applicability to contact 3-manifolds with boundary.

## Key findings

- Morse structures can be defined on partial open books.
- This extension aids in understanding contact manifolds with convex boundary.
- The framework generalizes previous Morse structure concepts.

## Abstract

The first author in recent work with D. Gay developed the notion of a Morse structure on an open book as a tool for studying closed contact 3-manifolds. We extend the notion of Morse structure to extendable partial open books in order to study contact 3-manifolds with convex boundary.