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Lefschetz Fixed Point Theorem and Intersection Homology

  • Mark Goresky
  • Robert MacPherson
Part of the Modern Birkhäuser Classics book series (MBC, volume 50)

Abstract

This article is a summary of the essential ingredients in [3]. We will consider a placid self-map with isolated fixed points on a subanalytic pseudomanifold and show that the trace of the induced homomorphism on intersection homology may be interpreted as a sum of certain linking numbers at the fixed points.

Keywords

Homology Class Lefschetz Number Intersection Cohomology Intersection Homology Multiplication Homomorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    A. Dold, Lectures on Algebraic Topology, Springer Verlag (New York) 1972.MATHGoogle Scholar
  2. [2]
    M. Goresky and R. MacPherson, Intersection homology II, Inv. Math. 71 (1983) pp. 77–129.CrossRefMathSciNetGoogle Scholar
  3. [3]
    M. Goresky and R. MacPherson, The Lefschetz fixed point theorem for intersection homology, to appear.Google Scholar
  4. [4]
    A. Grothendieck and L. Illusie, Formule de Lefschetz, in S. G. A. 5, Springer Lecture Notes in Mathematics # 589, Springer-Verlag, N.Y. 1977.Google Scholar

Copyright information

© Birkhäuser Boston, Inc. 1984

Authors and Affiliations

  • Mark Goresky
    • 1
  • Robert MacPherson
    • 2
  1. 1.Department of MathematicsNortheastern UniversityBostonUSA
  2. 2.Department of MathematicsBrown UniversityProvidenceUSA

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