We exploit the Galois symmetries of the little disks operads to show that many differentials in the Goodwillie–Weiss spectral sequences approximating the homology and homotopy of knot spaces vanish at a prime $p$. Combined with recent results on the relationship between embedding calculus and finite-type theory, we deduce that the $(n+1)$th Goodwillie–Weiss approximation is a $p$-local universal Vassiliev invariant of degree $\leq n$ for every $n \leq p + 1$.

中文翻译：

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结空间的Galois对称性

我们利用小圆盘的Galois对称性来证明，结点空间的同源性和同质性接近的Goodwillie-Weiss光谱序列中的许多差异在素数$ p $处消失。与嵌入微积分和有限型理论之间的关系最近的研究结果相结合，我们推断，$（N + 1）$个古德维利-韦斯近似是$ P $度-本地通用尤里耶维奇不变$ \当量N $为每$ n \ leq p + 1 $。