On the uniqueness of the fixed point index on differentiable manifolds
Fixed Point Theory and Applications volume 2004, Article number: 478686 (2004)
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.
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Furi, M., Pera, M.P. & Spadini, M. On the uniqueness of the fixed point index on differentiable manifolds. Fixed Point Theory Appl 2004, 478686 (2004). https://doi.org/10.1155/S168718200440713X