Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics

Jennifer Paulhus

ISBN 10: 1470460254 / ISBN 13: 9781470460259

Editore: American Mathematical Society, US, 2022

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Automorphism groups of Riemann surfaces have been widely studied for almost 150 years. This area has persisted in part because it has close ties to many other topics of interest such as number theory, graph theory, mapping class groups, and geometric and computational group theory. In recent years there has been a major revival in this area due in part to great advances in computer algebra systems and progress in finite group theory. This volume provides a concise but thorough introduction for newcomers to the area while at the same time highlighting new developments for established researchers. The volume starts with two expository articles. The first of these articles gives a historical perspective of the field with an emphasis on highly symmetric surfaces, such as Hurwitz surfaces. The second expository article focuses on the future of the field, outlining some of the more popular topics in recent years and providing 78 open research problems across all topics. The remaining articles showcase new developments in the area and have specifically been chosen to cover a variety of topics to illustrate the range of diversity within the field.

Codice articolo LU-9781470460259

Dati bibliografici

• Titolo: Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics
• Editore: American Mathematical Society, US
• Data di pubblicazione: 2022
• Lingua: Inglese
• ISBN 10: 1470460254
• ISBN 13: 9781470460259
• Rilegatura: Paperback
• Condizione: New
• Peso: 654 grammi

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Riassunto

The study of automorphism groups of Riemann surfaces is a classic and venerable area of mathematics that has enjoyed a recent surge of interest because of advances both in computer algebra systems and infinite group theory. An influx of new researchers is coinciding with the retirement of many pioneers in the field, and this collection of papers seeks to mark that transition with papers from researchers at all stages of their career. Among the topics are extending Harvey's surface kernel maps, planar representations of group actions on surfaces, arithmetic of dihedral origami, the reduction of super-elliptic Riemann surfaces, and the Riemann-Hurwitz formula for regular graph coverings. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)