Doklady Mathematics

, Volume 98, Issue 3, pp 629–633 | Cite as

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

  • V. A. VassilievEmail author


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 SmSM, 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. W. Anderson, Bull. Am. Math. Soc. 78, 784–786 (1972).CrossRefGoogle Scholar
  2. 2.
    V. I. Arnold, Transact. Moscow Math. Soc. 21, 30–52 (1970).Google Scholar
  3. 3.
    F. R. Cohen, R. L. Cohen, B. M. Mann, and R. L. Milgram, Acta Math. 166, 163–221 (1991).MathSciNetCrossRefGoogle Scholar
  4. 4.
    A. Kozlowski and K. Yamaguchi, J. Math. Soc. Jpn. 52 (4), 949–959 (2000).CrossRefGoogle Scholar
  5. 5.
    A. Kozlowski and K. Yamaguchi, Topol. Appl. 160 (1), 87–98 (2013).CrossRefGoogle Scholar
  6. 6.
    J. W. Milnor, Lectures on the h-Cobordism Theorem (Princeton Univ. Press, Princeton, 1965).CrossRefzbMATHGoogle Scholar
  7. 7.
    V. A. Vassiliev, Complements of Discriminants of Smooth Maps: Topology and Applications (Am. Math. Soc., Providence, RI, 1992).CrossRefGoogle Scholar
  8. 8.
    V. A. Vassiliev, Proc. Steklov Inst. Math. 290, 197–209 (2015).MathSciNetCrossRefGoogle Scholar
  9. 9.
    V. A. Vassiliev, Izv. Math. 80 (4), 791–810 (2016).MathSciNetCrossRefGoogle Scholar
  10. 10.
    V. A. Vassiliev, Dokl. Math. 96 (3), 616–619 (2017).MathSciNetCrossRefGoogle Scholar
  11. 11.
    V. A. Vassiliev, Dokl. Math. 98 (1), 330–333 (2018).CrossRefGoogle Scholar
  12. 12.
    V. A. Vassiliev, Homology of the Complex of not 2-Divisible Partitions, arXiv: 1807.05742.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia
  2. 2.National Research University Higher School of EconomicsMoscowRussia

Personalised recommendations