Equivariant Topology of Configuration Spaces
  We study the Fadell-Husseini index of the configuration space F(R^d,n) with respect to different subgroups of the symmetric group S_n. For p prime and d>0, we completely determine Index_{Z/p}(F(R^d,p);F_p) and partially describe Index{(Z/p)^k}(F(R^d,p^k);F_p). In this process we obtain results of independent interest, including:   (1) an extended equivariant Goresky-MacPherson formula,   (2) a complete description of the top homology of the partition lattice Pi_p as an F_p[Z_p]-module, and   (3) a generalized Dold theorem for elementary abelian groups.   The results on the Fadell-Husseini index yield a new proof of the Nandakumar & Ramana Rao conjecture for a prime. For n=p^k a prime power, we compute the Lusternik-Schnirelmann category cat(F(R^d,n)/S_n)=(d-1)(n-1). Moreover, we extend coincidence results related to the Borsuk-Ulam theorem, as obtained by Cohen & Connett, Cohen & Lusk, and Karasev & Volovikov. 
Pavle V. M. Blagojevi\'c, Wolfgang L\"uck, G\"unter M. Ziegler
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