General complete curve systems in boundary of 3-manifolds
Fengchun Lei, Xunbo Yin
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It is a well known theorem that a 3-manifold $M$ with a
Heegaard diagram $(V;J_1,\cdots,J_n)$ is a homotopy 3-sphere
if and only if there exists an embedding of $V$ in $S^3$ so
that $J_1,\cdots,J_n$ bound $n$ pairwise disjoint surfaces
$S_1,\cdots,S_n$ in $W=\overline{S^3-V}$. We may assume
$S_1,\cdots,S_n$ are incompressible in $W$. But in general,
we cannot assume that they are boundary incompressible,
since boundary compressions may yield surfaces with more
than one boundary component. We describe a version of above
theorem in which the involved surfaces are incompressible
and boundary incompressible in the corresponding manifold.
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