A generalized Lefschetz number for local Nielsen fixed point theory

Axioms for a local Reidemeister trace in fixed point and coincidence theory on differentiable manifolds

“…The existence of a local Reidemeister trace in fixed point theory for connected finite dimensional locally compact polyhedra is established by Fares and Hart in [5]. There, the slightly more general local H-Reidemeister trace is defined, called "the local generalized H-Lefschetz number".…”

“…In [5], the additivity and homotopy axioms are proved in Proposition 3.2.9 and Proposition 3.2.8, respectively. A strong version of the lift invariance axiom (see our Theorem 6) is proved in Proposition 3.2.4.…”

“…A local Reidemeister trace for fixed point theory was given by Fares and Hart in [5], but no Reidemeister trace (local or otherwise) has appeared in the literature for coincidence theory.…”

A fixed point index for equivariant maps

“…In fact, let s : ZR(f ) → R be the unique map which sends the function φ : R(f ) → Z to its equivalence class in R. Then by definition s(L(f )) = I(f ). For details on the generalized Lefschetz number, and its local version, the standard references are [13] and [11].…”

A Note on Equivariant Fixed Point Theory

“…A definition of local Reidemeister trace (in terms of Dennis traces of cellular chain maps) can be found also in [14]. Furthermore, in recent papers of W. Marzantowicz and C. Prieto [39,38] a definition equivalent to the definition of taut maps (which are there are named co-normal maps) is proposed and used on the problem of classification of G-maps (see also [19] on the subject).…”