Foundations of Hyperbolic Manifolds
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. Particular emphasis has been placed on readability and completeness of ar gument. The treatment of the mat
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Editorial Board l.R. Ewing P.W. Gehring P.R. Ralmos
Graduate Texts in Mathematics
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TAKEUTIlZARING. Introduction to Axiomatic Set Theory. 2nd ed. OXTOBY. Measure and Category. 2nd ed. SCHAEFFER. Topological Vector Spaces. HILTON/STAMMBACH. A Course in Homological Algebra. MAC LANE. Categories for the Working Mathematician. HUGHES/PiPER. Projective Planes. SERRE. A Course in Arithmetic. TAKEUTIlZAruNG. Axiometic Set Theory. HUMPHREYS. Introduction to Lie Algebras and Representation Theory. COHEN. A Course in Simple Homotopy Theory. CONWAY. Functions of One Complex Variable. 2nd ed. BEALs. Advanced Mathematical Analysis. ANDERSONlFuLLER. Rings and Categories of Modules. 2nd ed. GOLUBITSKy/GUILEMIN. Stable Mappings and Their Singularities. BERBERIAN. Lectures in Functional Analysis and Operator Theory. WINTER. The Structure of Fields. ROSENBLATT. Random Processes. 2nd ed. HALMOS. Measure Theory. HALMOS. A Hilbert Space Problem Book. 2nd ed. HUSEMOLLER. Fibre Bundles. 3rd ed. HUMPHREYS. Linear Algebraic Groups. BARNES/MAcK. An Algebraic Introduction to Mathematical Logic. GREUB. Linear Algebra. 4th ed. HOLMEs. Geometric Functional Analysis and Its ApplicatIons. HEWITT/STROMBERG. Real and Abstract Analysis. MANES. Algebraic Theories. KELLEY. General Topology. ZARISKIISAMUEL. Commutative Algebra. Vol. I. ZARISKI/SAMUEL. Commutative Algebra. Vol. TI. JACOBSON. Lectures in Abstract Algebra I. Basic Concepts. JACOBSON. Lectures in Abstract Algebra II. Linear Algebra. JACOBSON. Lectures in Abstract Algebra 111. Theory of Fields and Galois Theory. HIRSCH. Differential Topology. SPITZER. Principles of Random Walk. 2nd ed. WERMER. Banach Algebras and Several Complex Variables. 2nd ed. KELLEy/NAMIOKA et al. Linear Topological Spaces. MONK. Mathematical Logic. GRAUERT/FRITZscHE. Several Complex Variables. ARVESON. An Invitation to C*-Algebras. KEMENY/SNELL/KNAPP. Denumerable Markov Chains. 2nd ed. APOSTOL. Modular Functions and Dirichlet Series in Number Theory. 2nd ed. SERRE. Linear Representations of Finite Groups. GILLMAN/JERISON. Rings of Continuous Functions. KENDIG. Elementary Algebraic Geometry. LoiNE. Probability Theory r. 4th ed. LoEVE. Probability Theory II. 4th ed. MOISE. Geometric Topology in Dimensions 2 and 3. continued after index
John G. Ratcliffe
Foundations of Hyperbolic Manifolds With 164 Illustrations
Springer Science+Business Media, LLC
John G. Ratcliffe Department of Mathematics Vanderbilt University Nashville, TN 37240 USA Editorial Board J.H. Ewing Department of Mathematics Indiana University Bloomington, IN 47405 USA
F.W. Gehring Department of Mathematics University of Michigan Ann Arbor, MI 48109 USA
ISBN 978-0-387-94348-0 DOI 10.1007/978-1-4757-4013-4
P.R. Halmos Department of Mathematics Santa Clara University Santa Clara, CA 95053 USA
ISBN 978-1-4757-4013-4 (eBook)
Mathematics Subject Classifications (1991): 51-01, 51MI0, 52A20, 57M50, 20HlO, 30F40 Library
