Fixed Point Theory and Applications
Volume 2004 (2004), Issue 4, Pages 251-259
doi:10.1155/S168718200440713X
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
Abstract
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.