Discontinuous Groups of Isometries in the Hyperbolic Plane

Author: Werner Fenchel,Jakob Nielsen

Publisher: Walter de Gruyter

ISBN: 9783110175264

Category: Mathematics

Page: 364

View: 1244

"This is an introductory textbook on isometry groups of the hyperbolic plane. Interest in such groups dates back more than 120 years. - Examples appear in number theory (modular groups and triangle groups), the theory of elliptic functions, and the theory of linear differential equations in the complex domain (giving rise to the alternative name Fuchsian groups.). - "It is intended for students and researchers in the many areas of mathematics that involve the use of discontinuous groups."--Jacket.

Group Actions on Manifolds

Author: Reinhard Schultz

Publisher: American Mathematical Soc.

ISBN: 0821850385

Category: Mathematics

Page: 568

View: 3911

Not merely an account of new results, this book is also a guide to motivation behind present work and potential future developments. Readers can obtain an overall understanding of the sorts of problems one studies in group actions and the methods used to study such problems. The book will be accessible to advanced graduate students who have had the equivalent of three semesters of graduate courses in topology; some previous acquaintance with the fundamentals of transformation groups is also highly desirable. The articles in this book are mainly based upon lectures at the 1983 AMS-IMS-SIAM Joint Summer Research Conference, Group Actions on Manifolds, held at the University of Colorado. A major objective was to provide an overall account of current knowledge in transformation groups; a number of survey articles describe the present state of the subject from several complementary perspectives. The book also contains some research articles, generally dealing with results presented at the conference. Finally, there is a discussion of current problems on group actions and an acknowledgment of the work and influence of D. Montgomery on the subject.

Discrete Groups and Geometry

Author: Conference on discrete groups and geometry,W. J. Harvey

Publisher: Cambridge University Press

ISBN: 9780521429320

Category: Mathematics

Page: 248

View: 7912

This volume contains a selection of refereed papers presented in honour of A.M. Macbeath, one of the leading researchers in the area of discrete groups. The subject has been of much current interest of late as it involves the interaction of a number of diverse topics such as group theory, hyperbolic geometry, and complex analysis.

Spaces of Homotopy Self-Equivalences - A Survey

Author: John W. Rutter

Publisher: Springer

ISBN: 3540691359

Category: Mathematics

Page: 170

View: 5251

This survey covers groups of homotopy self-equivalence classes of topological spaces, and the homotopy type of spaces of homotopy self-equivalences. For manifolds, the full group of equivalences and the mapping class group are compared, as are the corresponding spaces. Included are methods of calculation, numerous calculations, finite generation results, Whitehead torsion and other areas. Some 330 references are given. The book assumes familiarity with cell complexes, homology and homotopy. Graduate students and established researchers can use it for learning, for reference, and to determine the current state of knowledge.

The complex analytic theory of Teichmüller spaces

Author: Subhashis Nag

Publisher: Wiley-Interscience


Category: Mathematics

Page: 427

View: 8163

An accessible, self-contained treatment of the complex structure of the Teichm?ller moduli spaces of Riemann surfaces. Complex analysts, geometers, and especially string theorists (!) will find this work indispensable. The Teichm?ller space, parametrizing all the various complex structures on a given surface, itself carries (in a completely natural way) the complex structure of a finite- or infinite-dimensional complex manifold. Nag emphasizes the Bers embedding of Teichm?ller spaces and deals with various types of complex-analytic co?rdinates for them. This is the first book in which a complete exposition is given of the most basic fact that the Bers projection from Beltrami differentials onto Teichm?ller space is a complex analytic submersion. The fundamental universal property enjoyed by Teichm?ller space is given two proofs and the Bers complex boundary is examined to the point where totally degenerate Kleinian groups make their spectacular appearance. Contains much material previously unpublished.