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arXiv · 1004.0746

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

Jesus Gonzalez·Peter Landweber
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Abstract

We compute the integral homology and cohomology groups of configuration spaces of two distinct points on a given real projective space. The explicit answer is related to the (known multiplicative structure in the) integral cohomology---with simple and twisted coefficients---of the dihedral group of order 8 (in the case of unordered configurations) and the elementary abelian 2-group of rank 2 (in the case of ordered configurations). As an application, we complete the computation of the symmetric topological complexity of real projective spaces of dimension 2^i + d for d=0,1,2.

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Jesus Gonzalez, Peter Landweber. 2010-04-06. The integral cohomology groups of configuration spaces of pairs of points in real projective spaces. https://arxiv.org/abs/1004.0746

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