arXiv subjects

Qiang E

Publications and source records attributed to Qiang E.

5 recordsLinked to original sources

arXiv2024

On the weak reducing pairs in critical Heegaard splitting

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.

math.GT↗

arXiv2022

On Heegaard splittings with finite many pairs of disjoint compression disks

Suppose $V\cup_S W$ is a weakly reducible Heegaard splitting of a closed 3-manifold which admits only $n$ pairs of disjoint compression disks on distinct sides and $g>2$. We show $V\cup_S W$ admits an untelescoping: $(V_1\cup_{S_1}W_1)\cup_F(W_2\cup_{S_2}V_2)$ such that $W_i$ has only one separating compressing disk and $d(S_i)\geq 2$, for $i=1,~2$. If $n>1$, at least one of $d(S_i)$ is 2 and $S$ is a critical Heegaard surface.

math.GT↗

arXiv2017

On keen weakly reducbile Heegaard splittings

A Heegaard splitting which admits a unique pair of disjoint compression disks on distinct sides is said to be keen weakly reducible. This paper provides an construction of keen weakly reducible Heegaard splittings of arbitrary genus except 2. Furthermore, critical Heegaard splittings may yield if we change some conditions.

math.GT↗

arXiv2013

A proof of Lickorish and Wallace's theorem

In this paper, we give a simple proof of Lickorish and Wallace's theorem, which states that every closed orientable 3-manifold is obtained by surgery on some link in 3-sphere.

math.GT↗

arXiv2013

Critical Heegaard surfaces obtained by self-amalgamation

Critical surfaces can be regarded as topological index 2 minimal surfaces which was introduced by David Bachman. In this paper we give a sufficient condition and a necessary condition for self-amalgamated Heegaard surfaces to be critical.

math.GT↗