English

On the weak reducing pairs in critical Heegaard splitting

Geometric Topology 2024-12-06 v2

Abstract

A weak reducing pair in a Heegaard splitting M = V \cup_S W is a pair of disjoint essential disks D \in V and E \in W. The weakly reducible Heegaard splitting contains at least one weak reducing pair. Critical Heegaard splitting is a special case of weakly reducible Heegaard splitting which contains at least two weak reducing pairs satisfying some special conditions. In this paper, we discuss the properties of weak reducing pairs in a critical Heegaard splitting and give a necessary condition for Heegaard surface to be critical.

Keywords

Cite

@article{arxiv.2404.18382,
  title  = {On the weak reducing pairs in critical Heegaard splitting},
  author = {Dongqi Sun and Qiang E},
  journal= {arXiv preprint arXiv:2404.18382},
  year   = {2024}
}

Comments

There are some contents that need further improvement