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Author:   Werner Fenchel ,  Jakob Nielsen ,  Asmus L. Schmidt
Publisher:   De Gruyter
Imprint:   De Gruyter
Volume:   29
Dimensions:   Width: 15.50cm , Height: 2.50cm , Length: 23.00cm
Weight:   0.796kg
ISBN:  

9783110175264

ISBN 10:   3110175266
Pages:   385
Publication Date:   16 December 2002
Recommended Age:   College Graduate Student
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

Editor's preface - Short biography of the authors - Mobius transformations and non-euclidean geometry - Pencils of circles - Inversive geometry - Cross-ratio - Mobius tranformations, direct and reversed - Invariant points and classification of Mobius transformations - Complex distance of two pairs of points - Non-Euclidian metric - Geometric transformations - Non-Euclidean trigonometry - Products and commutators of motions - Discontinuous groups of motions and reversions - The concept of discontinuity - Groups with invariant points or lines - A discontinuity theorem - F-groups. Fundamental set and limit set - The Convex domain of F-group. Characteristic and isometric neighbourhood - Quasi-compactness modulo F and finite generation of F - Surfaces associated with discontinuous groups - The surfaces D modulo G and K(F) modulo F - Area and type numbers - Decompositions of groups - Composition of groups - Decomposition of groups - Decompositions of F-groups containing reflections - Elementary groups and elementary surfaces - Complete decomposition and normal form in the case of quasi-compactness - Exhaustion in the case of non-quasi-compactness - Isomorphism and homeomorphism - Topological and geometrical isomorphism - Topological and geometrical homeomorphism - Construction of g-mappings. Metric parameters. Congruent groups - Symbols and definitions - Bibliography

Reviews

The Fenchel-Nielsen manuscript has been famous for a long time already and its final publication is a valuable edition to mathematical literature. EMS Newsletter Those working in the field will be grateful to the editor Asmus Schmidt for producing this classic text; it can now be cited without the annoying reference 'Fenchel an Nielsen (to appear)'. David Singerman in: Bulletin of the London Mathematical Society 36/2004

Author Information

Asmus L. Schmidt is Associate Professor at the Institute for Mathematical Sciences of the University of Copenhagen, Denmark.

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