The Delta-Nielsen number in products

In 1967 Robert F. Brown derived a formula which relates the Nielsen number N(f) of a fibre map f to the Nielsen numbers N(f),(fb), where f,fb are induced by f. This work is concerned to prove an analogous result for the Δ-Nielsen number, N(f,g,Δ). In Chapter I we introduce the set of coincidences of two maps f,g: X->Γ,f(f,g) = {xϵX: f(x)=g(x)}. We partition this set into equivalence classes by means of the equivalence relation of fixed end-point homotopy and then study some of the geometry of the equivalence classes. We then proceed to introduce the Δ-Nielsen number N(f,g,Δ) by means of an index, which we show satisfies the axioms of Brooks [1969] for a coincidence index. Thereafter we show N(f,g,Δ) to be a homotopy invariant. In Chapter II we introduce the class of fibre spaces. By restricting ourselves to fibre spaces which are products of closed, finitely triangulable manifolds, we derive an analogous formula for coincidences as Brown has for fixed points. Some suggestions for a complete analogue conclude the work.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

1973

Author dc:creator

• Mordant, Ian

Advisor dc:contributor.advisor

• Schlagbauer, H

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/22233

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/22233