The Lefschetz-Hopf Theory
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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.
KeywordsNatural Transformation Lefschetz Number Fixed Point Index Singular Homology Lefschetz Theorem
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