Fox-Neuwirth cell structures and the cohomology of symmetric groups

We use the Fox-Neuwirth cell structure for one-point compactifications of configuration spaces as the starting point for understanding our recent calculation of the mod-two cohomology of symmetric groups. We then use that calculation to give short proofs of classical results on this cohomology due to Nakaoka and to Madsen. v2. Added references, expanded exposition on the cochain model and a mathematical correction in the final section. v3. Added references.