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Geometric actions of the absolute Galois group
Thesis (MSc (Mathematics))--University of Stellenbosch, 2006.
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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Stellenbosch : University of Stellenbosch
2006
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| _version_ | 1867613759116148736 |
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| access_status_str | Open Access |
| author | Joubert, Paul |
| author2 | Breuer, Florian |
| author_browse | Breuer, Florian Joubert, Paul |
| author_facet | Breuer, Florian Joubert, Paul |
| author_sort | Joubert, Paul |
| collection | Thesis |
| dc_rights_str_mv | University of Stellenbosch |
| description | Thesis (MSc (Mathematics))--University of Stellenbosch, 2006. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/2508 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:41:14.564Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2006 |
| publishDateRange | 2006 |
| publishDateSort | 2006 |
| publisher | Stellenbosch : University of Stellenbosch |
| publisherStr | Stellenbosch : University of Stellenbosch |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/2508 Geometric actions of the absolute Galois group Joubert, Paul Breuer, Florian University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. Dissertations -- Mathematics Theses -- Mathematics Galois theory Geometric group theory Algebraic fields Thesis (MSc (Mathematics))--University of Stellenbosch, 2006. This thesis gives an introduction to some of the ideas originating from A. Grothendieck's 1984 manuscript Esquisse d'un programme. Most of these ideas are related to a new geometric approach to studying the absolute Galois group over the rationals by considering its action on certain geometric objects such as dessins d'enfants (called stick figures in this thesis) and the fundamental groups of certain moduli spaces of curves. I start by defining stick figures and explaining the connection between these innocent combinatorial objects and the absolute Galois group. I then proceed to give some background on moduli spaces. This involves describing how Teichmuller spaces and mapping class groups can be used to address the problem of counting the possible complex structures on a compact surface. In the last chapter I show how this relates to the absolute Galois group by giving an explicit description of the action of the absolute Galois group on the fundamental group of a particularly simple moduli space. I end by showing how this description was used by Y. Ihara to prove that the absolute Galois group is contained in the Grothendieck-Teichmuller group. 2006-10-12T07:16:43Z 2010-06-01T08:50:47Z 2006-10-12T07:16:43Z 2010-06-01T08:50:47Z 2006-03 Thesis http://hdl.handle.net/10019.1/2508 en University of Stellenbosch 762840 bytes application/pdf application/pdf Stellenbosch : University of Stellenbosch |
| spellingShingle | Dissertations -- Mathematics Theses -- Mathematics Galois theory Geometric group theory Algebraic fields Joubert, Paul Geometric actions of the absolute Galois group |
| title | Geometric actions of the absolute Galois group |
| title_full | Geometric actions of the absolute Galois group |
| title_fullStr | Geometric actions of the absolute Galois group |
| title_full_unstemmed | Geometric actions of the absolute Galois group |
| title_short | Geometric actions of the absolute Galois group |
| title_sort | geometric actions of the absolute galois group |
| topic | Dissertations -- Mathematics Theses -- Mathematics Galois theory Geometric group theory Algebraic fields |
| url | http://hdl.handle.net/10019.1/2508 |
| work_keys_str_mv | AT joubertpaul geometricactionsoftheabsolutegaloisgroup |