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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...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613184997720065 |
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| access_status_str | Open Access |
| author | Mordant, Ian |
| author2 | Schlagbauer, H |
| author_browse | Mordant, Ian Schlagbauer, H |
| author_facet | Schlagbauer, H Mordant, Ian |
| author_sort | Mordant, Ian |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/22233 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:07.214Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/22233 The Delta-Nielsen number in products Mordant, Ian Schlagbauer, H Mathematics 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. 2016-10-21T07:32:52Z 2016-10-21T07:32:52Z 1973 Master Thesis Masters MSc http://hdl.handle.net/11427/22233 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Mordant, Ian The Delta-Nielsen number in products |
| thesis_degree_str | Master's |
| title | The Delta-Nielsen number in products |
| title_full | The Delta-Nielsen number in products |
| title_fullStr | The Delta-Nielsen number in products |
| title_full_unstemmed | The Delta-Nielsen number in products |
| title_short | The Delta-Nielsen number in products |
| title_sort | delta nielsen number in products |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/22233 |
| work_keys_str_mv | AT mordantian thedeltanielsennumberinproducts AT mordantian deltanielsennumberinproducts |