The Reidemeister Trace of an $n$-valued map

TL;DR

This paper extends the Reidemeister trace, a topological fixed point invariant, to n-valued maps on polyhedra, generalizing classical properties and establishing an averaging formula.

Contribution

It introduces the Reidemeister trace for n-valued maps, generalizing fixed point invariants to multi-valued functions on polyhedra.

Findings

Defined Reidemeister trace for n-valued maps.

Proved properties generalizing single-valued case.

Established an averaging formula for the invariant.

Abstract

In topological fixed point theory, the Reidemeister trace is an invariant associated to a selfmap of a polyhedron which combines information from the Lefschetz and Nielsen numbers. In this paper we define the Reidemeister trace in the context of $n$-valued selfmaps of compact polyhedra. We prove several properties of the Reidemeister trace which generalize properties from the single-valued theory, and prove an averaging formula.