On orbit configuration spaces of spheres

The orbit configuration space FZ2(Sk,n) is the space of all ordered n-tuples of points on the k-sphere such that no two of them are identical or antipodal. The cohomology algebra of FZ2(Sk,n), with integer coefficients, is here determined completely, and described in terms of generators, bases and relations. To this end, we analyze the cohomology spectral sequence of a fibration FZ2(Sk,n)→Sk, where the fiber—in contrast to the situation for the classical configuration space F(Sk,n)—is not the complement of a linear subspace arrangement. Analogies to the arrangement case, however, are crucial for getting a complete description of its cohomology.