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The integral cohomology of configuration spaces of pairs of points in real projective spaces
-
Carlos Domínguez
,
Jesús González
Published/Copyright:
August 3, 2011
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 
with 
and 
.
Keywords: 2-point configurations of real projective spaces; dihedral group of order 8; Bockstein spectral sequence; symmetric topological complexity; Euclidean embedding dimension
Received: 2011-06-28
Published Online: 2011-08-03
Published in Print: 2013-11-01
© 2013 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Continuity of homomorphisms into power-associative complete normed algebras
- The connection problem associated with a Selberg type integral and the q-Racah polynomials
- The space of linear maps into a Grassmann manifold
- The integral cohomology of configuration spaces of pairs of points in real projective spaces
- The tree of irreducible numerical semigroups with fixed Frobenius number
- The topological decomposition of inverse limits of iterated wreath products of finite Abelian groups
- Comparison principles and Dirichlet problem for fully nonlinear degenerate equations of Monge–Ampère type
