The Bennequin number, Kauffman polynomial, and ruling invariants of a Legendrian link: the Fuchs conjecture and beyond
The Bennequin number, Kauffman polynomial, and ruling invariants of a Legendrian link: the Fuchs conjecture and beyond
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贝内金数、考夫曼多项式和勒让德联系的统治不变量：福克斯猜想及其他猜想
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发表时间：
2005
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通讯作者：
Dan Rutherford
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作者：
Dan Rutherford
我们证明了Legendrian环的非分次规则不变量可以被实现为Kauffman多项式的某些非零系数当且仅当由Kauffman多项式给出的Bennequin数的上界是尖锐的。这肯定地解决了富克斯的一个猜想。用类似的方法证明了一个由HOMFLY多项式和2-分次规则给出的上界的结果。
We show that the ungraded ruling invariants of a Legendrian link can be realized as certain coefficients of the Kauffman polynomial which are non-vanishing if and only if the upper bound for the Bennequin number given by the Kauffman polynomial is sharp. This resolves positively a conjecture of Fuchs. Using similar methods a result involving the upper bound given by the HOMFLY polynomial and 2-graded rulings is proved.