One-sided Heegaard splittings of non-Haken 3-manifolds

TL;DR

This paper discusses properties of one-sided Heegaard splittings in non-Haken 3-manifolds but has been withdrawn due to a flaw in its main proof, with some content expanded in subsequent papers.

Contribution

It initially aimed to classify and analyze structural properties of one-sided Heegaard splittings in non-Haken 3-manifolds, though the main results are not confirmed.

Findings

Main theorems are invalid due to proof flaw

Structural properties are detailed in subsequent papers

Classification results are expanded in later work

Abstract

This paper has been withdrawn by the author, as the proof of Theorem 3.2 contains a flaw; subsequently, both it and Theorem 3.3 are not known to hold. The content of Section 5 has been improved and expanded upon in two separate papers. The structural properties in 5.1 and 5.2 appear in arXiv:1101.2603; the classification in 5.3 in arxiv:1101.2890. Please refer to Proposition 4.4 in the former as a reference for arXiv:0807.4795v1.