# The complexity of orientable graph manifolds

## TL;DR

This paper establishes an upper bound for the Matveev complexity of all closed connected orientable prime graph manifolds, confirming its sharpness for a large catalog of such manifolds.

## Contribution

It provides a universal upper bound for the complexity of orientable prime graph manifolds and verifies its sharpness across a comprehensive catalog.

## Key findings

- Upper bound for Matveev complexity established
- Bound is sharp for all cataloged manifolds
- Enhances understanding of manifold complexity measures

## Abstract

We give an upper bound for the Matveev complexity of the whole class of closed connected orientable prime graph manifolds that is sharp for all 14502 graph manifolds of the Recognizer catalogue (available at \texttt{http://matlas.math.csu.ru/?page=search}).