Lefschetz Fixed Point Theorem and Intersection Homology

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


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.


Homology Class Lefschetz Number Intersection Cohomology Intersection Homology Multiplication Homomorphism 
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  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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