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| On 3-Submanifolds of S^3 Which Admit CompleteSpanning Curve Systems |
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Citation： |
Yan ZHAO,Fengchun LEI,Fengling LI.On 3-Submanifolds of S^3 Which Admit CompleteSpanning Curve Systems[J].Chinese Annals of Mathematics B,2017,38(6):1373~1380 |
| Page view： 1118
Net amount： 1318 |
Authors： |
Yan ZHAO; Fengchun LEI;Fengling LI |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11329101, 11431009, 11329101, 11471151,
11401069) and the grant of the Fundamental Research Funds for the
Central Universities (No.DUT14LK12). |
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| Abstract： |
Let $M$ be a compact connected $3$-submanifold of the 3-sphere $S^3$
with one boundary component $F$ such that there exists a collection
of $n$ pairwise disjoint connected orientable surfaces $\mathcal
S=\{S_1,\cdots, S_n\}$ properly embedded in $M$, $\partial{\mathcal
S}=\{\partial S_1,\cdots, \partial S_n\}$ is a complete curve system
on $F$. We call $\mathcal S$ a complete surface system for $M$, and
$\partial \mathcal{S}$ a complete spanning curve system for $M$. In
the present paper, the authors show that the equivalent classes of
complete spanning curve systems for $M$ are unique, that is, any
complete spanning curve system for $M$ is equivalent to $\partial
\mathcal S$. As an application of the result, it is shown that the
image of the natural homomorphism from the mapping class group
${\mathcal M}(M)$ to ${\mathcal M}(F)$ is a subgroup of the
handlebody subgroup ${\mathcal H}_n$. |
Keywords： |
Complete surface system, Complete spanning curve system, Heegaard
diagram, Handlebody addition |
Classification： |
57M99 |
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