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Volume 27, Issue 1
A Lower Bound of the Genus of a Self-Amalgamated 3-Manifolds

Xu Li & Fengchun Lei

Commun. Math. Res., 27 (2011), pp. 47-52.

Published online: 2021-05

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  • Abstract

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 $F'$ of $∂M'$, and $F' − Q_1 ∪ Q_2$ is connected. We give a lower bound to the Heegaard genus of $M$ when $M'$ has a Heegaard splitting with sufficiently high distance.

  • Keywords

self-amalgamation, distance, Heegaard genus.

  • AMS Subject Headings

57M99

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CMR-27-47, author = {Li , Xu and Lei , Fengchun}, title = {A Lower Bound of the Genus of a Self-Amalgamated 3-Manifolds}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {27}, number = {1}, pages = {47--52}, abstract = {

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 $F'$ of $∂M'$, and $F' − Q_1 ∪ Q_2$ is connected. We give a lower bound to the Heegaard genus of $M$ when $M'$ has a Heegaard splitting with sufficiently high distance.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19105.html} }
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 -

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 $F'$ of $∂M'$, and $F' − Q_1 ∪ Q_2$ is connected. We give a lower bound to the Heegaard genus of $M$ when $M'$ has a Heegaard splitting with sufficiently high distance.

Li , Xu and Lei , Fengchun. (2021). A Lower Bound of the Genus of a Self-Amalgamated 3-Manifolds. Communications in Mathematical Research . 27 (1). 47-52. doi:
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