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Author : Thomas Breuer
Publisher : Unknown
Page : 199 pages
File Size : 50,8 Mb
Release : 1998
Category : Electronic
ISBN : OCLC:633252078
Author : Thomas Breuer
Publisher : Cambridge University Press
Page : 216 pages
File Size : 43,8 Mb
Release : 2000-09-21
Category : Mathematics
ISBN : 0521798094
Addresses a topic from classical analysis using modern algebraic and computational tools. For graduates and researchers.
Author : Emilio Bujalance,Jose J. Etayo,Jose M. Gamboa,Grzegorz Gromadzki
Publisher : Springer
Page : 214 pages
File Size : 42,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540471806
This research monograph provides a self-contained approach to the problem of determining the conditions under which a compact bordered Klein surface S and a finite group G exist, such that G acts as a group of automorphisms in S. The cases dealt with here take G cyclic, abelian, nilpotent or supersoluble and S hyperelliptic or with connected boundary. No advanced knowledge of group theory or hyperbolic geometry is required and three introductory chapters provide as much background as necessary on non-euclidean crystallographic groups. The graduate reader thus finds here an easy access to current research in this area as well as several new results obtained by means of the same unified approach.
Author : Emilio Bujalance García,Emilio Bujalance
Publisher : Lecture Notes in Mathematics
Page : 228 pages
File Size : 51,9 Mb
Release : 1990-09-12
Category : Mathematics
ISBN : UOM:39015049372231
This research monograph provides a self-contained approach to the problem of determining the conditions under which a compact bordered Klein surface S and a finite group G exist, such that G acts as a group of automorphisms in S. The cases dealt with here take G cyclic, abelian, nilpotent or supersoluble and S hyperelliptic or with connected boundary. No advanced knowledge of group theory or hyperbolic geometry is required and three introductory chapters provide as much background as necessary on non-euclidean crystallographic groups. The graduate reader thus finds here an easy access to current research in this area as well as several new results obtained by means of the same unified approach.
Author : Aaron Wootton,S. Allen Broughton,Jennifer Paulhus
Publisher : American Mathematical Society
Page : 366 pages
File Size : 55,5 Mb
Release : 2022-02-03
Category : Mathematics
ISBN : 9781470460259
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.
Author : William Thomas Kiley
Publisher : Unknown
Page : 114 pages
File Size : 41,7 Mb
Release : 1969
Category : Group theory
ISBN : CORNELL:31924001110927
Author : R.D.M. Accola
Publisher : Springer
Page : 109 pages
File Size : 49,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540376026
Author : Emilio Bujalance,Emilio Bujalance García,Francisco Javier Cirre,José Manuel Gamboa,Grzegorz Gromadzki
Publisher : Springer Science & Business Media
Page : 181 pages
File Size : 54,6 Mb
Release : 2010-10-06
Category : Mathematics
ISBN : 9783642148279
This monograph deals with symmetries of compact Riemann surfaces. A symmetry of a compact Riemann surface S is an antianalytic involution of S. It is well known that Riemann surfaces exhibiting symmetry correspond to algebraic curves which can be defined over the field of real numbers. In this monograph we consider three topics related to the topology of symmetries, namely the number of conjugacy classes of symmetries, the numbers of ovals of symmetries and the symmetry types of Riemann surfaces.
Author : Grzegorz Gromadzki
Publisher : Unknown
Page : 212 pages
File Size : 40,6 Mb
Release : 1993
Category : Automorphisms
ISBN : CORNELL:31924074546924
Author : Gareth A. Jones,Jürgen Wolfart
Publisher : Springer
Page : 259 pages
File Size : 44,5 Mb
Release : 2016-03-23
Category : Mathematics
ISBN : 9783319247113
This volume provides an introduction to dessins d'enfants and embeddings of bipartite graphs in compact Riemann surfaces. The first part of the book presents basic material, guiding the reader through the current field of research. A key point of the second part is the interplay between the automorphism groups of dessins and their Riemann surfaces, and the action of the absolute Galois group on dessins and their algebraic curves. It concludes by showing the links between the theory of dessins and other areas of arithmetic and geometry, such as the abc conjecture, complex multiplication and Beauville surfaces. Dessins d'Enfants on Riemann Surfaces will appeal to graduate students and all mathematicians interested in maps, hypermaps, Riemann surfaces, geometric group actions, and arithmetic.
Author : Robert D.M. Accola
Publisher : Springer
Page : 117 pages
File Size : 41,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540490562
The book's main concern is automorphisms of Riemann surfaces, giving a foundational treatment from the point of view of Galois coverings, and treating the problem of the largest automorphism group for a Riemann surface of a given genus. In addition, the extent to which fixed points of automorphisms are generalized Weierstrass points is considered. The extremely useful inequality of Castelnuovo- Severi is also treated. While the methods are elementary, much of the material does not appear in the current texts on Riemann surfaces, algebraic curves. The book is accessible to a reader who has had an introductory course on the theory of Riemann surfaces or algebraic curves.
Author : Emilio Bujalance,Francisco Javier Cirre,José Manuel Gamboa,Grzegorz Gromadzki
Publisher : Springer
Page : 164 pages
File Size : 41,9 Mb
Release : 2010-09-29
Category : Mathematics
ISBN : 9783642148286
This monograph covers symmetries of compact Riemann surfaces. It examines the number of conjugacy classes of symmetries, the numbers of ovals of symmetries and the symmetry types of Riemann surfaces.
Author : Ernesto Girondo,Gabino González-Diez
Publisher : Cambridge University Press
Page : 311 pages
File Size : 40,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9780521519632
An elementary account of the theory of compact Riemann surfaces and an introduction to the Belyi-Grothendieck theory of dessins d'enfants.
Author : Rick Miranda
Publisher : American Mathematical Soc.
Page : 390 pages
File Size : 54,6 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821802687
The book was easy to understand, with many examples. The exercises were well chosen, and served to give further examples and developments of the theory. --William Goldman, University of Maryland In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking center stage. But the main examples come from projective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Duality Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves and cohomology are introduced as a unifying device in the latter chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one semester of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-semester course in complex variables or a year-long course in algebraic geometry.
Author : Benson Farb,Richard Hain,Eduard Looijenga
Publisher : American Mathematical Soc.
Page : 371 pages
File Size : 49,8 Mb
Release : 2013-08-16
Category : Mathematics
ISBN : 9780821898871
Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmüller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
