Abstract
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.
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© 2003 Springer Science+Business Media New York
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Granas, A., Dugundji, J. (2003). The Lefschetz-Hopf Theory. In: Fixed Point Theory. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21593-8_6
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DOI: https://doi.org/10.1007/978-0-387-21593-8_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1805-5
Online ISBN: 978-0-387-21593-8
eBook Packages: Springer Book Archive