TY - JOUR
T1 - A Sufficient Condition for the Genus of an Annulus Sum of Two 3-Manifolds to Be Non-Degenerate
AU - Li , Fengling
AU - Lei , Fengchun
JO - Communications in Mathematical Research 
VL - 1
SP - 85
EP - 96
PY - 2021
DA - 2021/05
SN - 26
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19180.html
KW - Heegaard genus, annulus sum, distance.
AB - <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>