On knotted real projective planes
On knotted real projective planes
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在有结的实射影平面上
DOI：
10.1142/s0218216515400118
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Akio Kawauchi
中科院分区：
文献类型：
--
作者：
Yongju Bae;Seonmi Choi; Akio Kawauchi
Let $L\xrightarrow{\mathfrak{B}} L_{\mathfrak{B}}$ be a hyperbolic transformation. Let B be a new band attaching to L such that $L_{B} \xrightarrow{\mathfrak{B}} L_{\mathfrak{B}\cup \{B\}}$ is also a hyperbolic transformation. In this paper, we will study the relationship between the realizing surfaces $F(L\xrightarrow{\mathfrak{B}} L_{\mathfrak{B}})$ and $F(L_{B} \xrightarrow{\mathfrak{B}} L_{\mathfrak{B}\cup \{B\}})$. If B is a noncoherent band to both L andsuch that $\hat{F}(L_{B} \xrightarrow{\mathfrak{B}} L_{\mathfrak{B}\cup \{B\}})$ is defined, then $\hat{F}(L \xrightarrow{\mathfrak{B}} L_{\mathfrak{B}})~\sharp~ {\mathbf{R}}P^{2}$ and $\hat{F}(L_{B} \xrightarrow{\mathfrak{B}} L_{\mathfrak{B}\cup \{B\}})~\sharp~ {\mathbf{R}}P^{2}$ are ambient isotopic, whereRP2is one of the standard real projective planes. We will study the triviality of $\hat{F}(L_{B} \xrightarrow{\mathfrak{B}} L_{\mathfrak{B}\cup \{B\}})$ because as an application,RP2can untangle some knotted sphere $\hat{F}(L \xrightarrow{\mathfrak{B}} L_{\mathfrak{B}})$ with suitable conditions, when it is attached to $\hat{F}(L \xrightarrow{\mathfrak{B}} L_{\mathfrak{B}})$ by the connected sum.
