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

2010/04/05 by Jesús González, Peter S. Landweber, Gonzalez, Jesus +1
Computer Science · Mathematics · #55M30 #55R80 #55T10 #57R19 #57R40 #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1004.0746

openalex publication_date 2010/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the integral homology and cohomology groups of configuration\nspaces of two distinct points on a given real projective space. The explicit\nanswer is related to the (known multiplicative structure in the) integral\ncohomology---with simple and twisted coefficients---of the dihedral group of\norder 8 (in the case of unordered configurations) and the elementary abelian\n2-group of rank 2 (in the case of ordered configurations). As an application,\nwe complete the computation of the symmetric topological complexity of real\nprojective spaces of dimension 2ⁱ + d for d=0,1,2.\n

Citations

• The Cohomology Algebra of Unordered Configuration Spaces
• Einlagerung von Mannigfaltigkeiten in euklidische R�ume

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