Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivariant Cohomology of Configuration Spaces mod 2: The State of the
  Art   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, Blagojevi\'c,
L\"uck \& 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.

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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org