The fixed point index of topological fixed point theory is a well studied integer-valued algebraic invariant of a mapping which can be characterized by a small set of axioms. The coincidenceindex is an extension of the concept to topological (Nielsen) coincidence theory. We demonstrate that three natural axioms are sufficient to characterize the coincidenceindex in the setting of continuous mappings on oriented differentiablemanifolds, the most common setting for Nielsen coincidence theory.
Topology and its Applications
Staecker, Christopher P., "On the uniqueness of the coincidence index on orientable differentiable manifolds" (2007). Math & Computer Science Faculty Publications. 30.
Staecker, P. Christopher, On the uniqueness of the coincidence index on orientable differentiable manifolds. Topology and its Applications, 154 2007, 1961–1970.