Comprehensive introduction to the geometric and topological structure of Kleinian groups. Starts with Möbius transformations acting on the (extended) complex plane. The next chapter concerns discrete groups of hyperbolic isometries in nspace. This part ends with a discussion of elementary Kleinian groups, and the Fuchsian groups. The second part of the book treats more advanced topics such as geometrically finite groups.
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Inside This Book
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First Sentence:
In this chapter we review the basic properties of fractional linear transformations. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
accidental parabolic transformations, simple disjoint loops, invariant horoball, part with signature, elliptic cyclic, branched universal, parabolic cyclic, cusped region, quasifuchsian group, side pairing transformations, geometrically finite subgroup, hyperbolic cyclic, planarity theorem, primitive parabolic element, parabolic fixed point, same basic signature, unmarked sphere, fundamental polyhedron, parabolic pair, distinct translates, loxodromic element, isometric circle, maximal cyclic subgroup, spanning disc, fractional reflections Key Phrases - Capitalized Phrases (CAPs): (learn more)
Combinatorial Group Theory, Abelian Kleinian, Loxodromic Cyclic Constructions, Panels Defined, Rigidity of Triangle Groups, Strings of Beads, The Euclidean Groups, The Finite Groups New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this chapter we review the basic properties of fractional linear transformations. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
accidental parabolic transformations, simple disjoint loops, invariant horoball, part with signature, elliptic cyclic, branched universal, parabolic cyclic, cusped region, quasifuchsian group, side pairing transformations, geometrically finite subgroup, hyperbolic cyclic, planarity theorem, primitive parabolic element, parabolic fixed point, same basic signature, unmarked sphere, fundamental polyhedron, parabolic pair, distinct translates, loxodromic element, isometric circle, maximal cyclic subgroup, spanning disc, fractional reflections Key Phrases - Capitalized Phrases (CAPs): (learn more)
Combinatorial Group Theory, Abelian Kleinian, Loxodromic Cyclic Constructions, Panels Defined, Rigidity of Triangle Groups, Strings of Beads, The Euclidean Groups, The Finite Groups New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 58
books:
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54
books
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- Complex Manifolds and Deformation of Complex Structures (Classics in Mathematics) by Kunihiko Kodaira in Back Matter
- Introduction to Modular Forms (Grundlehren der mathematischen Wissenschaften) by Serge Lang in Back Matter
- Ordinary Differential Equations (Universitext) by Vladimir I. Arnold in Back Matter
- Entropy, Large Deviations, and Statistical Mechanics (Classics in Mathematics) by Richard Ellis in Back Matter
- Theory of Group Representations (Grundlehren der mathematischen Wissenschaften) by M.A. Naimark in Back Matter
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- Hyperbolic Manifolds and Discrete Groups by Michael Kapovich on 4 pages
- Spaces of Kleinian Groups (London Mathematical Society Lecture Note Series) by Yair N. Minsky on 4 pages
- Quasiconformal Mappings and Analysis: A Collection of Papers Honoring F.W. Gehring by Peter Duren on page 241, page 250, and page 251
- Discontinuous Groups of Isometries in the Hyperbolic Plane (De Gruyter Studies in Mathematics) by W. Fenchel in Back Matter (1), and Back Matter (2)
- Algebraic Theory of the Bianchi Groups (Chapman & Hall/CRC Pure and Applied Mathematics) by Fine in Back Matter (1), and Back Matter (2)
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