The Markov theorems for spatial graphs and handlebody-knots with Y-orientations
The Markov theorems for spatial graphs and handlebody-knots with Y-orientations
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空间图和 Y 方向把手结的马尔可夫定理
DOI：
10.1142/s0129167x15501165
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Atsushi Ishii
中科院分区：
文献类型：
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作者：
Scott Carter;Atsushi Ishii;Masahico Saito;Kokoro Tanaka;南 範彦;矢ヶ崎達彦;Atsushi Ishii
我们建立了空间图和手柄结的马尔可夫定理。我们引入了 IH 标记的空间三价图并在其上发展了理论，因为空间图和手柄体结都可以实现为 IH 标记的空间三价图的 IH 等价类。我们证明，没有源和汇的图的任何两个方向都通过局部方向变化的有限序列相关，保留了图没有源和汇的条件。这导致我们为 IH 标记的空间三价图定义两种方向，它们适合闭合辫子，并用于马尔可夫定理的证明。我们给出了定向缠结的增强亚历山大定理，该定理也用于证明。
We establish the Markov theorems for spatial graphs and handlebody-knots. We introduce an IH-labeled spatial trivalent graph and develop a theory on it, since both a spatial graph and a handlebody-knot can be realized as the IH-equivalence classes of IH-labeled spatial trivalent graphs. We show that any two orientations of a graph without sources and sinks are related by finite sequence of local orientation changes preserving the condition that the graph has no sources and no sinks. This leads us to define two kinds of orientations for IH-labeled spatial trivalent graphs, which fit a closed braid, and is used for the proof of the Markov theorem. We give an enhanced Alexander theorem for orientated tangles, which is also used for the proof.