On normalizations of a regular isotopy invariant for spatial graphs
On normalizations of a regular isotopy invariant for spatial graphs
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空间图正则同位素不变量的归一化
DOI：
10.1142/s0129167x1100729x
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发表时间：
2011
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：
Miki Hirano;Taku Ishii and Tadashi Miyazaki;Taku Ishii and Tomonori Moriyama;Taku Ishii;石井卓;永野 幸一;Koichi Nagano;永野幸一;永野 幸一;Atsushi Ishii
给出了空间图的正则同位素不变量的归一化框架，并引入了在局部移动下满足相同关系的多个归一化。对于几乎所有没有桥的三价图的空间嵌入，我们对Yamada多项式进行了规范化，并从skein关系、有限类型不变量和Yamada多项式的求值的角度看到了利用我们的规范化的好处。我们证明了两个归一化之间的差异的集合是一个完全的空间图同调不变量。
We give a framework to normalize a regular isotopy invariant of a spatial graph, and introduce many normalizations satisfying the same relation under a local move. We normalize the Yamada polynomial for spatial embeddings of almost all trivalent graphs without a bridge, and see the benefit to utilize our normalizations from the viewpoint of skein relations, the finite type invariants, and evaluations of the Yamada polynomial. We show that the collection of the differences between two of our normalizations is a complete spatial-graph-homology invariant.