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A contribution to the foundations of the theory of Quasifibration
The concept of quasifibration was invented by Dold and Thom (DT]. May (M2] approached quasifibrations from a new angle, making use of n-equivalences. This dissertation presents a study of the notion of n-equivalences and related types of maps. The first of our two main goals is to prove a result, Th...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2023
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| _version_ | 1867613283967565824 |
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| access_status_str | Open Access |
| author | Witbooi, Peter Joseph |
| author2 | Hardie, K. A. |
| author_browse | Hardie, K. A. Witbooi, Peter Joseph |
| author_facet | Hardie, K. A. Witbooi, Peter Joseph |
| author_sort | Witbooi, Peter Joseph |
| collection | Thesis |
| description | The concept of quasifibration was invented by Dold and Thom (DT]. May (M2] approached quasifibrations from a new angle, making use of n-equivalences. This dissertation presents a study of the notion of n-equivalences and related types of maps. The first of our two main goals is to prove a result, Theorem 5.1, which generalizes the fundamental theorem (DT; Satz 2.2] by Dold and Thom on globalization of quasifibrations. Secondly we show that by means of adjunction or clutching constructions, this theorem enables us to retrieve the famous results of James (J2; Theorem 1.2 and Theorem 1.3] in his work on suspension of spheres. The results of James appear in the thesis as Theorem 13.8. For some of the applications we need a generalized version of n-equivalence. This generalization entails replacing, in the definition of n-equivalence, the isomorphisms by isomorphisms modulo a suitable Serre class [Se] of abelian groups. For the sake of having the thesis self-contained, we include a formal discussion of localization of 1-connected spaces and Serre classes of abelian groups. This summarizes the scope of the thesis. More detail on the content of the thesis will be given after we have sketched a historical perspective on quasifibrations. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/38591 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:41.762Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| 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:11427/38591 A contribution to the foundations of the theory of Quasifibration Witbooi, Peter Joseph Hardie, K. A. mathematics and applied mathematics The concept of quasifibration was invented by Dold and Thom (DT]. May (M2] approached quasifibrations from a new angle, making use of n-equivalences. This dissertation presents a study of the notion of n-equivalences and related types of maps. The first of our two main goals is to prove a result, Theorem 5.1, which generalizes the fundamental theorem (DT; Satz 2.2] by Dold and Thom on globalization of quasifibrations. Secondly we show that by means of adjunction or clutching constructions, this theorem enables us to retrieve the famous results of James (J2; Theorem 1.2 and Theorem 1.3] in his work on suspension of spheres. The results of James appear in the thesis as Theorem 13.8. For some of the applications we need a generalized version of n-equivalence. This generalization entails replacing, in the definition of n-equivalence, the isomorphisms by isomorphisms modulo a suitable Serre class [Se] of abelian groups. For the sake of having the thesis self-contained, we include a formal discussion of localization of 1-connected spaces and Serre classes of abelian groups. This summarizes the scope of the thesis. More detail on the content of the thesis will be given after we have sketched a historical perspective on quasifibrations. 2023-09-13T13:24:08Z 2023-09-13T13:24:08Z 1995 2023-09-13T13:06:11Z Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/38591 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science |
| spellingShingle | mathematics and applied mathematics Witbooi, Peter Joseph A contribution to the foundations of the theory of Quasifibration |
| thesis_degree_str | Doctoral |
| title | A contribution to the foundations of the theory of Quasifibration |
| title_full | A contribution to the foundations of the theory of Quasifibration |
| title_fullStr | A contribution to the foundations of the theory of Quasifibration |
| title_full_unstemmed | A contribution to the foundations of the theory of Quasifibration |
| title_short | A contribution to the foundations of the theory of Quasifibration |
| title_sort | contribution to the foundations of the theory of quasifibration |
| topic | mathematics and applied mathematics |
| url | http://hdl.handle.net/11427/38591 |
| work_keys_str_mv | AT witbooipeterjoseph acontributiontothefoundationsofthetheoryofquasifibration AT witbooipeterjoseph contributiontothefoundationsofthetheoryofquasifibration |