Garside-theoretic analysis of Burau representations

Garside-theoretic analysis of Burau representations
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Burau 表示的 Garside 理论分析

DOI：
10.1142/s0218216517500407
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发表时间：
2017
期刊：
J. Knot Theory Ramification
影响因子：
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通讯作者：
Matthieu Calvez and Tetsuya Ito
Matthieu Calvez and Tetsuya Ito
中科院分区：
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文献类型：
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作者：
Tomonori Fukunaga;Masatomo Takahashi;Tetsuya Ito;福永　知則;Tetsuya Ito;福永　知則;Tomonori Fukunaga;Matthieu Calvez and Tetsuya Ito

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我们建立了辫子群的经典和对偶Garside结构与Burau表示之间的关系。利用经典结构，我们制定了一个非零准则的4股辫子群的Burau表示。在对偶情形下，证明了任意辫子指数的Burau表示在单套辫子集上是单射的.
We establish relations between both the classical and the dual Garside structures of the braid group and the Burau representation. Using the classical structure, we formulate a non-vanishing criterion for the Burau representation of the 4-strand braid group. In the dual context, it is shown that the Burau representation for arbitrary braid index is injective when restricted to the set ofsimply-nested braids.