TY - JOUR
T1 - A Lower Bound of the Genus of a Self-Amalgamated 3-Manifolds
AU - Li , Xu
AU - Lei , Fengchun
JO - Communications in Mathematical Research 
VL - 1
SP - 47
EP - 52
PY - 2021
DA - 2021/05
SN - 27
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19105.html
KW - self-amalgamation, distance, Heegaard genus.
AB - <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>