Heegaard splittings of graph manifolds

TL;DR

This paper introduces a method for constructing Heegaard splittings in oriented graph manifolds, which are 3-manifolds composed of Seifert-fibered pieces, focusing on the fully oriented case.

Contribution

It provides a novel construction technique for Heegaard splittings specifically tailored for oriented graph manifolds with orientable bases.

Findings

Method for constructing Heegaard splittings in oriented graph manifolds

Applicable to fully oriented cases with Seifert-fibered pieces

Enhances understanding of 3-manifold decompositions

Abstract

In this paper we give a method to construct Heegaard splittings of oriented graph manifolds with orientable bases. A graph manifold is a closed $3$-manifold admitting only Seifert-fibered pieces in its Jaco-Shalen decomposition; for technical reasons, we restrict our attention to the fully oriented case, i.e. both the pieces and the bases are oriented.