Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658185 | Topology and its Applications | 2015 | 32 Pages |
Let R be a commutative ring where 2 is invertible. We compute the R -cohomology ring of the configuration space Conf(RPm,k)Conf(RPm,k) of k ordered points in the m -dimensional real projective space RPmRPm. The method is based on the fact that the orbit configuration space of k ordered points in the m -dimensional sphere (with respect to the antipodal action) is a 2k2k-fold covering of Conf(RPm,k)Conf(RPm,k). This implies that, for odd m , the Leray spectral sequence for the inclusion Conf(RPm,k)⊂(RPm)kConf(RPm,k)⊂(RPm)k collapses after its first non-trivial differential, just as it does when RPmRPm is replaced by a complex projective variety. The method also allows us to handle the R-cohomology ring of the configuration space of k ordered points in the punctured manifold RPm−⋆RPm−⋆.