EXTENDING AUTOMORPHISMS OF THE GENUS-2 SURFACE OVER THE 3-SPHERE
EXTENDING AUTOMORPHISMS OF THE GENUS-2 SURFACE OVER THE 3-SPHERE
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DOI：
10.1093/qmathj/haz042
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发表时间：
2018-03
期刊：
影响因子：
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通讯作者：
Kenta Funayoshi;Yuya Koda
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文献类型：
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作者：
Kenta Funayoshi;Yuya Koda
一个闭合可定向曲面$\Sigma $的自同构$f$在3球$S^3$上是可扩展的，如果$f$扩展到对$(S^3, \Sigma)$关于某个嵌入$\Sigma \ hookrighrow S^3$的自同构$f$。我们证明了如果一个属2曲面$\Sigma $的自同构在$S^3$上是可扩展的，则$f$对嵌入$\Sigma \hookright - row S^3$可扩展到$(S^3, \Sigma)$对的自同构，使得$\Sigma $在两边都是属2柄体的边界。由于Ozawa的原因，嵌入$S^3$的2属柄体外部本质环的分类，第二作者起了关键作用。
An automorphism $f$ of a closed orientable surface $\Sigma $ is said to be extendable over the 3-sphere $S^3$ if $f$ extends to an automorphism of the pair $(S^3, \Sigma )$ with respect to some embedding $\Sigma \hookrightarrow S^3$. We prove that if an automorphism of a genus-2 surface $\Sigma $ is extendable over $S^3$, then $f$ extends to an automorphism of the pair $(S^3, \Sigma )$ with respect to an embedding $\Sigma \hookrightarrow S^3$ such that $\Sigma $ bounds genus-2 handlebodies on both sides. The classification of essential annuli in the exterior of genus-2 handlebodies embedded in $S^3$ due to Ozawa, and the second author plays a key role.