This systematic and self-contained treatment examines the topology of differentiable manifolds, curvature and homology of Riemannian manifolds, compact Lie groups, complex manifolds, and curvature and homology of Kaehler manifolds. It generalizes the theory of Riemann surfaces to that of Riemannian m... read more
See Sample Pages! Click here to look inside this book.
Customers who bought this book also bought:
Our Editors also recommend:
Cohomology Operations and Applications in Homotopy Theory by Robert E. Mosher, Martin C. Tangora This treatment explores the single most important variety of cohomology operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications. 1968 edition.
Differential Manifolds by Antoni A. Kosinski Introductory text for advanced undergraduates and graduate students presents systematic study of the topological structure of smooth manifolds, starting with elements of theory and concluding with method of surgery. 1993 edition.
Introduction to Differentiable Manifolds by Louis Auslander, Robert E. MacKenzie This text presents basic concepts in the modern approach to differential geometry. Topics include Euclidean spaces, submanifolds, and abstract manifolds; fundamental concepts of Lie theory; fiber bundles; and multilinear algebra. 1963 edition.
Tensor Analysis on Manifolds by Richard L. Bishop, Samuel I. Goldberg Balanced between formal and abstract approaches, this text covers function-theoretical and algebraic aspects, manifolds and integration theory, adaptation to classical mechanics, more. "First-rate." — American Mathematical Monthly. 1980 edition.
Topology of 3-Manifolds and Related Topics by M.K. Fort, Jr., Daniel Silver Summaries and full reports from a 1961 conference discuss decompositions and subsets of 3-space; n-manifolds; knot theory; the Poincaré conjecture; and periodic maps and isotopies. Familiarity with algebraic topology required. 1962 edition.
Algebraic Topology by C. R. F. Maunder Thorough, modern treatment, essentially from a homotopy theoretic viewpoint. Topics include homotopy and simplicial complexes, the fundamental group, homology theory, homotopy theory, homotopy groups and CW-Complexes, and other topics. Includes exercises. Bibliography. 1980 corrected edition.
Algebraic Topology: Homology and Cohomology by Andrew H. Wallace This self-contained treatment studies several algebraic invariants: the fundamental group, singular and Cech homology groups, and a variety of cohomology groups. Extensive appendixes review background material. 1970 edition.
An Introduction to Algebraic Topology by Andrew H. Wallace This self-contained treatment begins with three chapters on the basics of point-set topology, after which it proceeds to homology groups and continuous mapping, barycentric subdivision, and simplicial complexes. 1961 edition.
A Combinatorial Introduction to Topology by Michael Henle Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.
Counterexamples in Topology by Lynn Arthur Steen, J. Arthur Seebach, Jr. Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.
Differential Topology: An Introduction by David B. Gauld This text covers topological spaces and properties, some advanced calculus, differentiable manifolds, orientability, submanifolds and an embedding theorem, tangent spaces, vector fields and integral curves, Whitney's embedding theorem, more. Includes 88 helpful illustrations. 1982 edition.
Differential Topology: First Steps by Andrew H. Wallace Keeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. 1968 edition.
General Topology by Stephen Willard Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures.
A Geometric Introduction to Topology by C. T. C. Wall First course in algebraic topology for advanced undergraduates. Homotopy theory, the duality theorem, relation of topological ideas to other branches of pure mathematics. Exercises and problems. 1972 edition.
Introduction to Topology: Second Edition by Theodore W. Gamelin, Robert Everist Greene This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.
Invitation to Combinatorial Topology by Maurice Fréchet, Ky Fan, Howard W. Eves Elementary text, accessible to anyone with a background in high school geometry, covers problems inherent to coloring maps, homeomorphism, applications of Descartes' theorem, topological polygons, more. Includes 108 figures. 1967 edition.
Point Set Topology by Steven A. Gaal Suitable for a complete course in topology, this text also functions as a self-contained treatment for independent study. Additional enrichment materials make it equally valuable as a reference. 1964 edition.
Real Variables with Basic Metric Space Topology by Robert B. Ash Designed for a first course in real variables, this text encourages intuitive thinking and features detailed solutions to problems. Topics include complex variables, measure theory, differential equations, functional analysis, probability. 1993 edition.
Introduction to Topology: Third Edition by Bert Mendelson Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.
Topology: An Introduction with Application to Topological Groups by George McCarty Covers sets and functions, groups, metric spaces, topologies, topological groups, compactness and connectedness, function spaces, the fundamental group, the fundamental group of the circle, locally isomorphic groups, more. 1967 edition.
Topology and Geometry for Physicists by Charles Nash, Siddhartha Sen Written by physicists for physics students, this text assumes no detailed background in topology or geometry. Topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory. 1983 edition.
Topology for Analysis by Albert Wilansky Three levels of examples and problems make this volume appropriate for students and professionals. Abundant exercises, ordered and numbered by degree of difficulty, illustrate important topological concepts. 1970 edition.
Undergraduate Topology by Robert H. Kasriel This introductory treatment is essentially self-contained and features explanations and proofs that relate to every practical aspect of point set topology. Hundreds of exercises appear throughout the text. 1971 edition.
Topology: An Introduction to the Point-Set and Algebraic Areas by Donald W. Kahn Comprehensive coverage of elementary general topology as well as algebraic topology, specifically 2-manifolds, covering spaces and fundamental groups. Problems, with selected solutions. Bibliography. 1975 edition.
The Concept of a Riemann Surface by Hermann Weyl, Gerald R. MacLane This classic on the general history of functions combines function theory and geometry, forming the basis of the modern approach to analysis, geometry, and topology. 1955 edition.
Conformal Mapping on Riemann Surfaces by Harvey Cohn Lucid, insightful exploration reviews complex analysis, introduces Riemann manifold, shows how to define real functions on manifolds, and more. Perfect for classroom use or independent study. 344 exercises. 1967 edition.
Topology by John G. Hocking, Gail S. Young Superb one-year course in classical topology. Topological spaces and functions, point-set topology, much more. Examples and problems. Bibliography. Index.
The Riemann Zeta-Function: Theory and Applications by Aleksandar Ivic This text covers exponential integrals and sums, 4th power moment, zero-free region, mean value estimates over short intervals, higher power moments, omega results, zeros on the critical line, zero-density estimates, and more. 1985 edition.
Riemann's Zeta Function by H. M. Edwards Superb study of the landmark 1859 publication entitled "On the Number of Primes Less Than a Given Magnitude" traces the developments in mathematical theory that it inspired. Topics include Riemann's main formula, the Riemann-Siegel formula, more.
Product Description:
This systematic and self-contained treatment examines the topology of differentiable manifolds, curvature and homology of Riemannian manifolds, compact Lie groups, complex manifolds, and curvature and homology of Kaehler manifolds. It generalizes the theory of Riemann surfaces to that of Riemannian manifolds. Includes four helpful appendixes. "A valuable survey." — Nature. 1962 edition.
Reprint of the Academic Press, New York, 1962 edition.
This book was printed in the United States of America.
Dover books are made to last a lifetime. Our US book-manufacturing partners produce the highest quality books in the world and they create jobs for our fellow citizens. Manufacturing in the United States also ensures that our books are printed in an environmentally friendly fashion, on paper sourced from responsibly managed forests.
