The Lefschetz-Hopf Theory

  • Andrzej Granas
  • James Dugundji
Part of the Springer Monographs in Mathematics book series (SMM)


This chapter is algebraic in character. We develop here the homological tools needed to formulate and prove some of the central results in topological fixed point theory: (i) the Lefschetz fixed point theorem for various classes of maps of non-compact spaces, and (ii) the Hopf index theorem expressing the relation between the generalized Lefschetz number and the fixed point index for compact maps of ANRs. The chapter ends with a number of applications.


Natural Transformation Lefschetz Number Fixed Point Index Singular Homology Lefschetz Theorem 
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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Andrzej Granas
    • 1
    • 2
  • James Dugundji
  1. 1.Département de Mathématiques et StatistiqueUniversité de MontréalMontréalCanada
  2. 2.Department of Mathematics and Computer ScienceUniversity of Warmia and MazuryOlsztynPoland

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