The integral cohomology of configuration spaces of pairs of points in real projective spaces

Carlos Dominguez; Jesus Gonzalez; Peter Landweber

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arXiv · 1106.4593

The integral cohomology of configuration spaces of pairs of points in real projective spaces

Carlos Dominguez·Jesus Gonzalez·Peter Landweber

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Abstract

We compute the integral cohomology ring of configuration spaces of two points on a given real projective space. Apart from an integral class, the resulting ring is a quotient of the known integral cohomology of the dihedral group of order 8 (in the case of unordered configurations, thus has only 2- and 4-torsion) or of the elementary abelian 2-group of rank 2 (in the case of ordered configurations, thus has only 2-torsion). As an application, we complete the computation of the symmetric topological complexity of real projective spaces of dimensions of the form 2^i+j for non-negative i and j with j<3.

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Carlos Dominguez, Jesus Gonzalez, Peter Landweber. 2011-06-22. The integral cohomology of configuration spaces of pairs of points in real projective spaces. https://arxiv.org/abs/1106.4593

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