@Article{CMR-26-1,
author = {Li, Fengling and Lei, Fengchun},
title = {A Sufficient Condition for the Genus of an Annulus Sum of Two 3-Manifolds to Be Non-Degenerate},
journal = {Communications in Mathematical Research },
year = {2010},
volume = {26},
number = {1},
pages = {85--96},
abstract = {<p style="text-align: justify;">Let $M_i$ be a compact orientable 3-manifold, and $A_i$ a non-separating
incompressible annulus on a component of $∂M_i$, say $F_i
, i = 1, 2$. Let $h : A_1 → A_2$ be a homeomorphism, and $M = M_1 ∪_h M_2$, the annulus sum of $M_1$ and $M_2$ along $A_1$ and $A_2$. Suppose that $M_i$ has a Heegaard splitting $V_i ∪_{S_i} W_i$ with distance $d(S_i) ≥ 2g(M_i) + 2g(F_{3−i}) + 1, i = 1, 2$. Then $g(M) = g(M_1) + g(M_2)$, and the
minimal Heegaard splitting of $M$ is unique, which is the natural Heegaard splitting
of $M$ induced from $V_1 ∪_{S_1} W_1$ and $V_2 ∪_{S_2} W_2$.</p>},
issn = {2707-8523},
doi = {https://doi.org/2010-CMR-19180},
url = {https://global-sci.com/article/81897/a-sufficient-condition-for-the-genus-of-an-annulus-sum-of-two-3-manifolds-to-be-non-degenerate}
}