Regular maps


Thesis Type: Postgraduate

Institution Of The Thesis: Uludağ Üniversitesi, Turkey

Approval Date: 2007

Thesis Language: Turkish

Student: GAMZE SALTAN

Supervisor: İSMAİL NACİ CANGÜL

Abstract:

In this thesis, regular maps are considered and their classification on some surfaces of small genus is given. The regular maps on the sphere have been known since Kepler. Coxeter and Moser gave the classification of the regular maps on torus. Regular maps on orientable surfaces have, first, been defined in 1978 and all their properties are obtained. Regular maps on non-orientable surfaces are considered in recent years. Here we obtained the classification of all regular maps on surfaces up to genus 7. In the first chapter, some preliminaries necessary for the following chapters are recalled. In the second chapter, regular maps and the related notions are defined and some fundamental results are obtained. Further, the classification of all regular maps on surfaces up to genus 7 is given here. In the third chapter, the relation of regular maps with Hecke groups is given. Simply, knowing regular maps is equal to knowing normal subgroups of Hecke groups.