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On the Homotopy Property of Nussbaum's Fixed Point Index

Published online by Cambridge University Press:  20 November 2018

Gilles Fournier  and
Reine Fournier
Gilles Fournier
Affiliation:
Université de Sherbrooke, Sherbrooke, Québec
Reine Fournier
Affiliation:
Université de Sherbrooke, Sherbrooke, Québec
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In [14] R. D. Nussbaum generalized the fixed point index to a class of maps larger than the one in [5]. Unfortunately his homotopy property conditions are more restrictive than the often more readily verifiable ones of Eells-Fournier. In this paper we shall try to find an intermediate class of maps which will contain all the known examples of maps for which the index is defined and for which the condition of Eells-Fournier will imply the homotopy property.

In doing so, we shall give general conditions for which the sum of a compact map and a differentiable map will be a map having a fixed point index and for which the Lefschetz fixed point theorem is true.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 1 , 01 February 1982 , pp. 44 - 62
Copyright
Copyright © Canadian Mathematical Society 1982

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