Article
The engaging symmetry of Riemann surfaces: a historical perspective
Contemporary Mathematics, accepted
(2021)
Abstract
The historical development of Riemann surfaces, starting in the
late 1800's, was driven in large part by the study of highly symmetrical surfaces.
Not only do these surfaces have an engaging beauty, but they have very
strong interconnections with other structures such as maps on a surface. In
this expository article we fi rst develop the basics of Riemann surfaces and their
automorphism groups, laying out the tools for the historical treatment of the
highly symmetrical surfaces in the later sections. The main topics of the later
sections will be Hurwitz surfaces and groups, maps and dessins d'enfant on
surfaces, and platonic and quasi-platonic surfaces and groups. For the novice
reader, the introductory material will also be helpful background for reading
some of the other papers in this volume, particularly the companion article on
future directions in the fi eld.
Keywords
- Riemann surface,
- surface automorphism,
- triangle group,
- dessin d'enfant.
Disciplines
Publication Date
April 27, 2021
Citation Information
Sean A Broughton, Gareth A. Jones and David Singerman. "The engaging symmetry of Riemann surfaces: a historical perspective" Contemporary Mathematics, accepted (2021) Available at: http://works.bepress.com/allen_broughton/102/