








1. 
Record Nr. 
UNINA9910349325903321 


Autore 
Ratcliffe John G 


Titolo 
Foundations of Hyperbolic Manifolds / / by John G. Ratcliffe 





Pubbl/distr/stampa 


Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 









ISBN 

3030315975 
9783030315979 








Edizione 
[3rd ed. 2019.] 





Descrizione fisica 

1 online resource (xii, 800 pages) : illustrations 






Collana 

Graduate Texts in Mathematics, , 00725285 ; ; 149 






Disciplina 






Soggetti 

Geometry 
Topology 
Topological groups 
Lie groups 
Topological Groups, Lie Groups 








Lingua di pubblicazione 






Formato 
Materiale a stampa 





Livello bibliografico 
Monografia 





Nota di bibliografia 

Includes bibliographical references and index. 






Nota di contenuto 

Euclidean Geometry  Spherical Geometry  Hyperbolic Geometry  Inversive Geometry  Isometries of Hyperbolic Space  Geometry of Discrete Groups  Classical Discrete Groups  Geometric Manifolds  Geometric Surfaces  Hyperbolic 3Manifolds  Hyperbolic nManifolds  Geometrically Finite nManifolds  Geometric Orbifolds. 








Sommario/riassunto 

This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. This third edition greatly expands upon the second with an abundance of additional content, including a section dedicated to arithmetic hyperbolic groups. Over 40 new lemmas, theorems, and corollaries feature, along with more than 70 additional exercises. Color adds a new dimension to figures throughout. The book is divided into three parts. The first part is concerned with hyperbolic geometry and discrete groups. The main results are the characterization of hyperbolic reflection groups and Euclidean crystallographic groups. The second part is devoted to the theory of hyperbolic manifolds. The main results are Mostow’s rigidity theorem and the determination of the global geometry of hyperbolic manifolds of finite volume. The third part 










integrates the first two parts in a development of the theory of hyperbolic orbifolds. The main result is Poincaré’s fundamental polyhedron theorem. The exposition is at the level of a second year graduate student with particular emphasis placed on readability and completeness of argument. After reading this book, the reader will have the necessary background to study the current research on hyperbolic manifolds. From reviews of the second edition: Designed to be useful as both textbook and a reference, this book renders a real service to the mathematical community by putting together the tools and prerequisites needed to enter the territory of Thurston’s formidable theory of hyperbolic 3manifolds […] Every chapter is followed by historical notes, with attributions to the relevant literature, both of the originators of the idea present in the chapter and of modern presentation thereof. Victor V. Pambuccian, Zentralblatt MATH, Vol. 1106 (8), 2007. 





 