A Lefschetz Coincidence Theorem for Singular Varieties

  • J.-P. Brasselet
  • A. K. M. Libardi
  • T. F. M. Monis
  • E. C. Rizziolli
  • M. J. Saia
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 222)

Abstract

This article provides a survey concerning Lefschetz fixed point formula and Lefschetz coincidence formula in the smooth and singular cases, moreover we show a Lefschetz type formula for the Coincidence number of two maps. As a consequence we obtain a relation with correspondences, and we provide some examples.

Keywords

Coincidence Lefschetz fixed point theorem Intersection homology Singular varieties 

References

  1. 1.
    Bisi, C., Bracci, F., Izawa, T., Suwa, T.: Localized intersection of currents and the Lefschetz coincidence point theorem. arXiv:1406.0607v1
  2. 2.
    Borel, A., et al.: Intersection Cohomology. Progress in Mathematics, vol. 50. Swiss seminars, Boston (1984). ISBN 0-8176-3274-3Google Scholar
  3. 3.
    Brasselet, J.-P., Suwa, T.: Quelle coïncidence ! Preprint 2016Google Scholar
  4. 4.
    Brasselet, J.-P.: Définition combinatoire des homomorphismes de Poincaré, Alexander et Thom pour une pseudo-variété, Astérisque, pp. 82–83 (1981)Google Scholar
  5. 5.
    Goresky, M., MacPherson, R.: Intersection homology theory. Topology 19(2), 135–162 (1980)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Goresky, M., MacPherson, R.: Intersection homology II. Invent. Math. 72(1), 77–129 (1983)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Goresky, M., MacPherson, R.: Letschetz fixed point theorem for intersection homology. Comment. Math. Helvetici 60, 366–391 (1985)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Goresky, M., Pardon, W.: Wu numbers of singular spaces. Topology 28, 325–367 (1989)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Lefschetz, S.: Continuous transformations of manifolds Proc. Acad. Sci. USA 9, 90–93 (1923)CrossRefGoogle Scholar
  10. 10.
    MacPherson, R.: Intersection homology and perverse sheaves Report, December 15 1990, Colloquium Lecture notes distributed by AMS (1991)Google Scholar
  11. 11.
    Siegel, P.: Witt spaces: a geometric cycle theory for KO-homology at odd primes. Am. J. Math. 105(5), 1067–1105 (1983)CrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • J.-P. Brasselet
    • 1
    • 2
  • A. K. M. Libardi
    • 3
  • T. F. M. Monis
    • 3
  • E. C. Rizziolli
    • 3
  • M. J. Saia
    • 4
  1. 1.I2M Aix-Marseille UniversityMarseilleFrance
  2. 2.IBILCE-UNESPSão José do Rio Preto, S.P.Brasil
  3. 3.IGCE-UNESPRio Claro, S.P.Brasil
  4. 4.ICMC-USPSão Carlos, S.P.Brasil

Personalised recommendations