An Introduction to Algebraic Topology

An Introduction to Algebraic Topology

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.

Author: Andrew H. Wallace

Publisher: Courier Corporation

ISBN: 9780486152950

Category: Mathematics

Page: 208

View: 200

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.
Categories: Mathematics

Algebraic Topology

Algebraic Topology

Surveys several algebraic invariants, including the fundamental group, singular and Cech homology groups, and a variety of cohomology groups.

Author: Andrew H. Wallace

Publisher: Courier Corporation

ISBN: 9780486462394

Category: Mathematics

Page: 272

View: 613

Surveys several algebraic invariants, including the fundamental group, singular and Cech homology groups, and a variety of cohomology groups.
Categories: Mathematics

Algebraic Topology

Algebraic Topology

Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint.

Author: C. R. F. Maunder

Publisher: Courier Corporation

ISBN: 0486691314

Category: Mathematics

Page: 375

View: 276

Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. Author C.R.F. Maunder provides examples and exercises; and notes and references at the end of each chapter trace the historical development of the subject.
Categories: Mathematics

A Combinatorial Introduction to Topology

A Combinatorial Introduction to Topology

Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more.

Author: Michael Henle

Publisher: Courier Corporation

ISBN: 0486679667

Category: Mathematics

Page: 310

View: 838

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.
Categories: Mathematics

Topology

Topology

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.

Author: Donald W. Kahn

Publisher: Courier Corporation

ISBN: 0486686094

Category: Mathematics

Page: 217

View: 310

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.
Categories: Mathematics

Introduction to Topology

Introduction to Topology

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.

Author: Theodore W. Gamelin

Publisher: Courier Corporation

ISBN: 9780486320182

Category: Mathematics

Page: 256

View: 292

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.
Categories: Mathematics

A Geometric Introduction to Topology

A Geometric Introduction to Topology

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.

Author: Charles Terence Clegg Wall

Publisher: Courier Corporation

ISBN: 9780486678504

Category: Mathematics

Page: 168

View: 488

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.
Categories: Mathematics

Principles of Topology

Principles of Topology

Originally published: Philadelphia: Saunders College Publishing, 1989; slightly corrected.

Author: Fred H. Croom

Publisher: Courier Dover Publications

ISBN: 9780486801544

Category: Mathematics

Page: 336

View: 857

Originally published: Philadelphia: Saunders College Publishing, 1989; slightly corrected.
Categories: Mathematics

Homology Theory on Algebraic Varieties

Homology Theory on Algebraic Varieties

Concise and authoritative monograph, geared toward advanced undergraduate and graduate students, covers linear sections, singular and hyperplane sections, Lefschetz's first and second theorems, the Poincaré formula, and invariant and ...

Author: Andrew H. Wallace

Publisher: Courier Corporation

ISBN: 9780486799902

Category: Mathematics

Page: 128

View: 795

Concise and authoritative monograph, geared toward advanced undergraduate and graduate students, covers linear sections, singular and hyperplane sections, Lefschetz's first and second theorems, the Poincaré formula, and invariant and relative cycles. 1958 edition.
Categories: Mathematics

Elements of Point Set Topology

Elements of Point Set Topology

Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates.

Author: John D. Baum

Publisher: Courier Corporation

ISBN: 9780486668260

Category: Mathematics

Page: 150

View: 915

Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.
Categories: Mathematics

A First Course in Topology

A First Course in Topology

Numerous hints and figures illuminate the text. Dover (2014) republication of the edition originally published by The Williams & Wilkins Company, Baltimore, 1975. See every Dover book in print at www.doverpublications.com

Author: Robert A Conover

Publisher: Courier Corporation

ISBN: 9780486780016

Category: Mathematics

Page: 272

View: 597

Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects. Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text. Dover (2014) republication of the edition originally published by The Williams & Wilkins Company, Baltimore, 1975. See every Dover book in print at www.doverpublications.com
Categories: Mathematics

Introduction to Algebraic Geometry

Introduction to Algebraic Geometry

This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric.

Author: Serge Lang

Publisher: Courier Dover Publications

ISBN: 9780486834221

Category: Mathematics

Page: 272

View: 744

Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory. Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.
Categories: Mathematics

Topology

Topology

Throughout this text, a sustained geometric development functions as a single thread of reasoning that unifies the topological course.

Author: George McCarty

Publisher: Courier Corporation

ISBN: 9780486153049

Category: Mathematics

Page: 288

View: 616

"Admirably meets the topology requirements for the pregraduate training of research mathematicians."--American Mathematical Monthly Crucial to modern mathematics, topology is equally essential to many other disciplines, from quantum mechanics to sociology. This stimulating introduction employs the language of point set topology to define and discuss topological groups. The text examines set-theoretic topology and its applications in function spaces, as well as homotopy and the fundamental group. This new theoretical knowledge is applied to concrete problems, such as the calculation of the fundamental group of the circle and a proof of the fundamental theorem of algebra. The abstract development concludes with the classification of topological groups by equivalence under local isomorphism. Throughout this text, a sustained geometric development functions as a single thread of reasoning that unifies the topological course. Well-chosen exercises, along with a selection of problems in each chapter that contain interesting applications and further theory, help solidify students' working knowledge of topology and its applications.
Categories: Mathematics

Introduction to Topological Groups

Introduction to Topological Groups

Concise treatment covers semitopological groups, locally compact groups, Harr measure, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras. 1966 edition.

Author: Taqdir Husain

Publisher: Courier Dover Publications

ISBN: 9780486819198

Category: Mathematics

Page: 224

View: 819

Concise treatment covers semitopological groups, locally compact groups, Harr measure, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras. 1966 edition.
Categories: Mathematics

Algebraic Geometry

Algebraic Geometry

An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 ...

Author: Solomon Lefschetz

Publisher: Courier Corporation

ISBN: 9780486154725

Category: Mathematics

Page: 256

View: 233

An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Categories: Mathematics

General Topology

General Topology

Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students.

Author: Stephen Willard

Publisher: Courier Corporation

ISBN: 9780486131788

Category: Mathematics

Page: 384

View: 732

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.
Categories: Mathematics

Basic Algebraic Topology

Basic Algebraic Topology

[Joshi, 1983] K. D. Joshi, Introduction to General Topology, Wiley Eastern Ltd.,
New Delhi. ... 1968] R. E. Mosher and M. C. Tangora, Cohomology Operations
and Applications in Homotopy Theory, Dover Books in Mathematics. [Munkres,
2008] ...

Author: Anant R. Shastri

Publisher: CRC Press

ISBN: 9781466562448

Category: Mathematics

Page: 551

View: 725

Building on rudimentary knowledge of real analysis, point-set topology, and basic algebra, Basic Algebraic Topology provides plenty of material for a two-semester course in algebraic topology. The book first introduces the necessary fundamental concepts, such as relative homotopy, fibrations and cofibrations, category theory, cell complexes, and si
Categories: Mathematics

Lehrbuch der Topologie

Lehrbuch der Topologie

Author: Herbert Seifert

Publisher:

ISBN: OCLC:493389807

Category: Topology

Page: 353

View: 694

Categories: Topology

Introduction to Knot Theory

Introduction to Knot Theory

Hailed by the Bulletin of the American Mathematical Society as "a very welcome addition to the mathematical literature," this text is appropriate for advanced undergraduates and graduate students.

Author: Richard H. Crowell

Publisher:

ISBN: 0486468941

Category: Mathematics

Page: 182

View: 125

Hailed by the Bulletin of the American Mathematical Society as "a very welcome addition to the mathematical literature," this text is appropriate for advanced undergraduates and graduate students. Written by two internationally renowned mathematicians, its accessible treatment requires no previous knowledge of algebraic topology. Starting with basic definitions of knots and knot types, the text proceeds to examinations of fundamental and free groups. A survey of the historic foundation for the notion of group presentation is followed by a careful proof of the theorem of Tietze and several examples of its use. Subsequent chapters explore the calculation of fundamental groups, the presentation of a knot group, the free calculus and the elementary ideals, and the knot polynomials and their characteristic properties. The text concludes with three helpful appendixes and a guide to the literature.
Categories: Mathematics

Cohomology Operations and Applications in Homotopy Theory

Cohomology Operations and Applications in Homotopy Theory

Cohomology operations are at the center of a major area of activity in algebraic topology.

Author: Robert E. Mosher

Publisher: Courier Corporation

ISBN: 9780486466644

Category: Mathematics

Page: 214

View: 635

Cohomology operations are at the center of a major area of activity in algebraic topology. This treatment explores the single most important variety of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation. 1968 edition.
Categories: Mathematics