*This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb.*

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# A History of Algebraic and Differential Topology 1900 1960

This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet
# A History of Algebraic and Differential Topology 1900 1960

This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet
# Algebraic and Differential Topology

Algebraic and Differential Topology presents in a clear, concise, and detailed manner the fundamentals of homology theory. It first defines the concept of a complex and its Betti groups, then discusses the topolgoical invariance of a Betti group. The book next presents various applications of homology theory, such as mapping of polyhedrons onto other polyhedrons as well as onto themselves. The third volume in L.S. Pontryagin's Selected Works, this book provides as many insights into algebraic topology for today's mathematician as it did when the author was making his initial endeavors into this field.
# Algebraic and Differential Topology

Algebraic and Differential Topology presents in a clear, concise, and detailed manner the fundamentals of homology theory. It first defines the concept of a complex and its Betti groups, then discusses the topolgoical invariance of a Betti group. The book next presents various applications of homology theory, such as mapping of polyhedrons onto other polyhedrons as well as onto themselves. The third volume in L.S. Pontryagin's Selected Works, this book provides as many insights into algebraic topology for today's mathematician as it did when the author was making his initial endeavors into this field.
# Lectures on Algebraic and Differential Topology

# Lectures on Algebraic and Differential Topology

# Algebraic and Differential Topology of Robust Stability

In this book, two seemingly unrelated fields -- algebraic topology and robust control -- are brought together. The book develops algebraic/differential topology from an application-oriented point of view. The book takes the reader on a path starting from a well-motivated robust stability problem, showing the relevance of the simplicial approximation theorem and how it can be efficiently implemented using computational geometry. The simplicial approximation theorem serves as a primer to more serious topological issues such as the obstruction to extending the Nyquist map, K-theory of robust stabilization, and eventually the differential topology of the Nyquist map, culminating in the explanation of the lack of continuity of the stability margin relative to rounding errors. The book is suitable for graduate students in engineering and/or applied mathematics, academic researchers and governmental laboratories.
# Algebraic and Differential Topology Global Differential Geometry

"Papers written by eminent scientists from the international community on the occasion of the 90th anniversary of Marston Morse's birth"--T.p.
# Lectures on Algebraic and Differential Topology

# Reviews of Papers in Algebraic and Differential Topology Topological Groups and Homological Algebra

# L S Pontryagin Selected Works Algebraic and differential topology

# Lectures on Algebraic and Differential Topology

# Differential Forms in Algebraic Topology

Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.
# Introduction to Differential and Algebraic Topology

Topology as a subject, in our opinion, plays a central role in university education. It is not really possible to design courses in differential geometry, mathematical analysis, differential equations, mechanics, functional analysis that correspond to the temporary state of these disciplines without involving topological concepts. Therefore, it is essential to acquaint students with topo logical research methods already in the first university courses. This textbook is one possible version of an introductory course in topo logy and elements of differential geometry, and it absolutely reflects both the authors' personal preferences and experience as lecturers and researchers. It deals with those areas of topology and geometry that are most closely related to fundamental courses in general mathematics. The educational material leaves a lecturer a free choice in designing his own course or his own seminar. We draw attention to a number of particularities in our book. The first chap ter, according to the authors' intention, should acquaint readers with topolo gical problems and concepts which arise from problems in geometry, analysis, and physics. Here, general topology (Ch. 2) is presented by introducing con structions, for example, related to the concept of quotient spaces, much earlier than various other notions of general topology thus making it possible for students to study important examples of manifolds (two-dimensional surfaces, projective spaces, orbit spaces, etc.) as topological spaces, immediately.
# Reviews of Papers in Algebraic and Differential Topology Topological Groups and Homological Algebra

# Real Algebraic Differential Topology

# Algebraic Topology Via Differential Geometry

In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry.
# Differential Topology

"A very valuable book. In little over 200 pages, it presents a well-organized and surprisingly comprehensive treatment of most of the basic material in differential topology, as far as is accessible without the methods of algebraic topology....There is an abundance of exercises, which supply many beautiful examples and much interesting additional information, and help the reader to become thoroughly familiar with the material of the main text." —MATHEMATICAL REVIEWS
# Algebraic and Differential Topology

Algebraic and Differential Topology presents in a clear, concise, and detailed manner the fundamentals of homology theory. It first defines the concept of a complex and its Betti groups, then discusses the topolgoical invariance of a Betti group. The book next presents various applications of homology theory, such as mapping of polyhedrons onto other polyhedrons as well as onto themselves. The third volume in L.S. Pontryagin's Selected Works, this book provides as many insights into algebraic topology for today's mathematician as it did when the author was making his initial endeavors into this field.
# Lectures on algebraic and differential topology