@Article{CMR-27-1,
author = {Xu, Li and Lei, Fengchun},
title = {A Lower Bound of the Genus of a Self-Amalgamated 3-Manifolds},
journal = {Communications in Mathematical Research },
year = {2011},
volume = {27},
number = {1},
pages = {47--52},
abstract = {<p style="text-align: justify;">Let $M$ be a compact connected oriented 3-manifold with boundary, $Q_1, Q_2 ⊂ ∂M$ be two disjoint homeomorphic subsurfaces of $∂M$, and $h : Q_1 → Q_2$ be an orientation-reversing homeomorphism. Denote by $M_h$ or $M_{Q_1=Q_2}$ the 3-manifold obtained from $M$ by gluing $Q_1$ and $Q_2$ together via $h$. $M_h$ is called a
self-amalgamation of $M$ along $Q_1$ and $Q_2$. Suppose $Q_1$ and $Q_2$ lie on the same
component $F&#39;$ of $∂M&#39;$, and $F&#39; − Q_1 ∪ Q_2$ is connected. We give a lower bound to
the Heegaard genus of $M$ when $M&#39;$ has a Heegaard splitting with sufficiently high
distance.</p>},
issn = {2707-8523},
doi = {https://doi.org/2011-CMR-19105},
url = {https://global-sci.com/article/81854/a-lower-bound-of-the-genus-of-a-self-amalgamated-3-manifolds}
}