Flipping Heegaard splittings of Seifert fibered spaces

TL;DR

This paper investigates the conditions under which Heegaard splittings of Seifert fibered spaces can be flipped via isotopy, contributing to the understanding of their symmetries and structure.

Contribution

It provides a characterization of flippable Heegaard splittings specifically for Seifert fibered spaces, a topic not thoroughly explored before.

Findings

Identifies criteria for flippability of Heegaard splittings

Classifies flippable splittings in Seifert fibered spaces

Enhances understanding of symmetries in 3-manifold topology

Abstract

A Heegaard splitting of a $3$-manifold is flippable if there is an isotopy that interchanges the two sides of the Heegaard splitting. We explore which Heegaard splittings of Seifert fibered spaces are flippable.