论文标题
福克斯票房周期和第三次订单的瓦西尔不变
The Fox-Hatcher cycle and a Vassiliev invariant of order three
论文作者
论文摘要
我们表明，在Fox-hatcher 1-Cycles上r^3中长结空间1（x）的1（x）的整合产生了订单的Vassiliev不变性。该结果可以看作是第二名作者先前工作的延续，证明了Gramain 1-Cycles上I（x）的集成是Casson不变的，这是订单二的独特的非平凡的Vassiliev不变的不变的不变式（直至标量乘法）。本文的结果也类似于Mortier结果的一部分。我们的结果与Mortier的一个不同之处在于，但是由Mortier的一个动机，因为1循环I（x）是由与图形相关的配置空间积分给出的，而Mortier的Cocycle是以组合方式获得的。
We show that the integration of a 1-cocycle I(X) of the space of long knots in R^3 over the Fox-Hatcher 1-cycles gives rise to a Vassiliev invariant of order exactly three. This result can be seen as a continuation of the previous work of the second named author, proving that the integration of I(X) over the Gramain 1-cycles is the Casson invariant, the unique nontrivial Vassiliev invariant of order two (up to scalar multiplications). The result in the present paper is also analogous to part of Mortier's result. Our result differs from, but is motivated by, Mortier's one in that the 1-cocycle I(X) is given by the configuration space integrals associated with graphs while Mortier's cocycle is obtained in a combinatorial way.
