论文标题
配置空间的模棱两可的同学mod 2：最先进的状态
Equivariant Cohomology of Configuration Spaces mod 2: The State of the Art
论文作者
论文摘要
The equivariant cohomology of the classical configuration space $F(\mathbb{R}^d,n)$ has been been of great interest and has been studied intensively starting with the classical papers by Artin (1925/1947) on the theory of braids, by Fox and Neuwirth (1962), Fadell and Neuwirth (1962), and Arnol'd (1969).我们简要介绍了从开始到最近发展的主题。但是，如Hung（1990）的有影响力的论文中所述，我们关注经典配置空间的Mod 2 eprovariant同胞代数$ f（\ Mathbb {r}^d，n）$。我们以新的，详细的证明表明他的主要结果是正确的，但是悬挂在他的结果的道路上的论点不是，他的论文中的一些中间结果也是如此。 这使三位作者Blagojević，Lück\＆Ziegler（2016）的论文无效，后者使用了Hung（1990）的中间结果，以得出$ k $ ground and $ \ ell $ \ ell $ \ ell $ -skew嵌入的较低范围。利用我们对Hung的主要结果的新证明，我们为存在高度规则的嵌入而获得了新的下限：其中一些与以前声称的界限一致，有些人较弱。
The equivariant cohomology of the classical configuration space $F(\mathbb{R}^d,n)$ has been been of great interest and has been studied intensively starting with the classical papers by Artin (1925/1947) on the theory of braids, by Fox and Neuwirth (1962), Fadell and Neuwirth (1962), and Arnol'd (1969). We give a brief treatment of the subject from the beginnings to recent developments. However, we focus on the mod 2 equivariant cohomology algebras of the classical configuration space $F(\mathbb{R}^d,n)$, as described in an influential paper by Hung (1990). We show with a new, detailed proof that his main result is correct, but that the arguments that were given by Hung on the way to his result are not, as are some of the intermediate results in his paper. This invalidates a paper by three of the present authors, Blagojević, Lück \& Ziegler (2016), who used a claimed intermediate result from Hung (1990) in order to derive lower bounds for the existence of $k$-regular and $\ell$-skew embeddings. Using our new proof for Hung's main result, we get new lower bounds for existence of highly regular embeddings: Some of them agree with the previously claimed bounds, some are weaker.
