No abstract

It is shown that all the generalized Whitehead products vanish in X and all the components of X TA have the same homotopy type when X is a T-space. It is also shown that any T-space is a G-space. The dual spaces of T-spaces are introduced and studied.1991 Mathematics subject classification (Amer. Math. Soc): 55P45, 55P35.

Abstract. The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. Extending Ferrario's work on Reidemeister sets, we obtain algebraic results such as addition formulae for Reidemeister orbit sets. Similar formulae for Nielsen type essential orbit numbers are also proved for fibre preserving maps. Introduction. Nielsen fixed point theory has been extended to aNielsen type theory of periodic orbits [6, Section III.3]. In fixed point theory, the computation of the Nielsen number often relies on the knowledge of the Reidemeister set, that is, the set of Reidemeister conjugacy classes in the fundamental group. Ferrario [2] made an algebraic study of the Reidemeister set in relation to an invariant normal subgroup. He obtained addition formulae for Reidemeister numbers, and applied them to the Nielsen number of fibre preserving maps. Our aim in this paper is similar, but in the more complicated setting of periodic orbits: to study the Reidemeister orbit set of a group endomorphism in relation to an invariant normal subgroup, to obtain addition formulae for Reidemeister orbit numbers, and as application, to find addition formulae for Nielsen type essential orbit numbers of fibre preserving maps.Given a group endomorphism f : G → G, the Reidemeister set of f , denoted by R(f ), is the set of orbits of the left action of G on G via γ g → 2000 Mathematics Subject Classification: Primary 55M20.

No abstract

No abstract