D-classes de homotopia, uma generalização da teoria de Δ-classes de homotopia

Abstract

This work is based on Ph.d. thesis of R.Brooks [1]. R.Brooks develops his work in three parts, first establishes Nielsen s theory (Essential class, Nielsen s number, estimates for the Nielsen s number) for determined classes of pairs of homotopy, called _-classes of homotopy. In the second part using homology and cohomology develop an index, that associates to each tuple (f, A,B), a homomorphism L∗(f, A,B). In the third part he relates Nielsen s theory for _-classes of homotopy with the index theory of the second part. In this work we will extend to the concept of _-classes of homotopy for D-classes of homotopy, and will study the D-number of Nielsen, n(f, p,D), for (f, p) ∈ D, after that we will define an index, L∗(f, p, s(B)), with the objective to detect when n(f, p,D) > 0.