Fixed Point Theory and Applications
Volume 2004 (2004), Issue 4, Pages 251-259

On the uniqueness of the fixed point index on differentiable manifolds

Massimo Furi, Maria Patrizia Pera, and Marco Spadini

Dipartimento di Matematica Applicata‘G. Sansone’, Università degli Studi di Firenze, Via S. Marta 3, Florence 50139, Italy

Received 23 July 2004

Copyright © 2004 Massimo Furi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is well known that some of the properties enjoyed by the fixed point index can be chosen as axioms, the choice depending on the class of maps and spaces considered. In the context of finite-dimensional real differentiable manifolds, we will provide a simple proof that the fixed point index is uniquely determined by the properties of normalization, additivity, and homotopy invariance.