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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/2508 |
| Date | 03 1900 |
| Creators | Joubert, Paul |
| Contributors | Breuer, Florian, University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : University of Stellenbosch |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 762840 bytes, application/pdf |
| Rights | University of Stellenbosch |
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