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Twisted Homology of Configuration Spaces and Homology of Spaces of Equivariant Maps

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Abstract

We calculate homology groups with certain twisted coefficients of configuration spaces of projective spaces. This completes a calculation of rational homology groups of spaces of odd maps of spheres Sm → SM, m < M, and of the stable homology of spaces of non-resultant polynomial maps ℝm+1 → ℝM+1. Also, we calculate the homology of spaces of ℤr-equivariant maps of odd-dimensional spheres, and discuss further generalizations.

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Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, 119991, Russia

    V. A. Vassiliev

  2. National Research University Higher School of Economics, Moscow, 101000, Russia

    V. A. Vassiliev

Authors
  1. V. A. Vassiliev
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Correspondence to V. A. Vassiliev.

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Original Russian Text © V.A. Vassiliev, 2018, published in Doklady Akademii Nauk, 2018, Vol. 483, No. 6.

The article was translated by the author.

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Vassiliev, V.A. Twisted Homology of Configuration Spaces and Homology of Spaces of Equivariant Maps. Dokl. Math. 98, 629–633 (2018). https://doi.org/10.1134/S106456241807030X

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  • DOI: https://doi.org/10.1134/S106456241807030X

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