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Differential Forms in Algebraic Topology
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Raoul Bott, Loring W Tu
This text, developed from a first-year graduate course in algebraic topology, 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-and include some ...
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Introduction to Differentiable Manifolds
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Serge Lang
This book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. A certain number of concepts are essential for all three of these areas, and are so basic and elementary, that it is worthwhile to collect them together so that more advanced expositions can be given ...
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Differential Topology: First Steps
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Andrew 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. Its focus is the method of spherical modifications and the study of critical points of functions on manifolds. 1968 edition.
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Topology from the Differentiable Viewpoint
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John W Milnor
This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, ...
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Space-Filling Curves
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Hans Sagan
The subject of space-filling curves has generated a great deal of interest in the 100 years since the first such curve was discovered by Peano. Cantor, Hilbert, Moore, Knopp, Lebesgue, and Polya are among the prominent mathematicians who have contributed to the field. However, there have been no comprehensive treatments of the subject since ...
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Algebraic and Differential Topology of Robust Stability
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Edmond A Jonckheere
In this book, two seemingly unrelated fields - algebraic topology and robust control - are brought together. The book develops algebraic/differential topology proceeding from an easily motivated control engineering problem, showing the relevance of advanced topological concepts and reconstructing the fundamental concepts of algebraic/differential ...
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Introduction to differentiable manifolds
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Louis Auslander, Robert E MacKenzie
Algebraic geometry, complex variables, etc. Background in advanced calculus, point-set topology needed.
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Infinite Groups: Geometric, Combinatorial and Dynamical Aspects
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Laurent Bartholdi (Editor), Tullio Ceccherini-Silberstein (Editor), Tatiana Smirnova-Nagnibeda (Editor)
This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics addressed in the book include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p ...
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Topology of Fibre Bundles
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Norman Steenrod
Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics - such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically. It begins with a general introduction to bundles, including such ...
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Convex Integration Theory
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Professor David Spring (Editor), Smith
This book provides a comprehensive study of convex integration theory in immersion-theoretic topology. Convex integration theory, developed originally by M. Gromov, provides general topological methods for solving the h-principle for a wide variety of problems in differential geometry and topology, with applications also to PDE theory and to ...
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Complex, Contact and Symmetric Manifolds: In Honor of L. Vanhecke
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Oldrich Kowalski (Editor), Emilio Musso (Editor), Domenico Perrone (Editor)
This volume contains research and survey articles by well known and respected mathematicians on differential geometry and topology that have been collected and dedicated in honor of Lieven Vanhecke, as a tribute to his many fruitful and inspiring contributions to these fields. The papers, all written with the necessary introductory and contextual ...
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Differential Topology
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Morris W Hirsch
This book gives the reader a thorough knowledge of the basic topological ideas necessary for studying differential manifolds. These topics include immersions and imbeddings, approach techniques, and the Morse classification of surfaces and their cobordism. The author keeps the mathematical prerequisites to a minimum; this and the emphasis on the ...
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Foundations of Differential Geometry
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Shoshichi Kobayashi, Katsumi Nomizu
One of two volumes which lay the foundations for understanding differential geometry. This work familiarizes readers with various techniques of computation.
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Seminar on the Atiyah-Singer Index Theorem
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Richard S Palais
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A First Course in Geometric Topology and Differential Geometry
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Ethan Bloch
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The Novikov Conjecture: Geometry and Algebra
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by
Matthias Kreck
These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem. Then an introduction to surgery theory and a version of the assembly map is presented. Using the solution of the ...
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A History of Algebraic and Differential Topology, 1900-1960
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by
Jean Alexandre Dieudonne
A classic available again, this book traces the history of algebraic topology beginning with its creation by Henry Poincare in 1900, and describing in detail the important ideas introduced in the theory before 1960. In its first thirty years the field seemed limited to applications in algebraic geometry, but this changed dramatically in the 1930s ...
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Introduction to Differential Topology
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by
Th Brocker, K Janich, C B Thomas (Translator)
This book is intended as an elementary introduction to differential manifolds. The authors concentrate on the intuitive geometric aspects and explain not only the basic properties but also teach how to do the basic geometrical constructions. An integral part of the work are the many diagrams which illustrate the proofs. The text is liberally ...
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Elementary Differential Topology: Lectures Given at Massachusetts Institute of Technology Fall, 1961
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James R. Munkres
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String Topology and Cyclic Homology
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by
Ralph L Cohen, Kathryn Hess, Alexander A Voronov
The subject of this book is string topology, Hochschild and cyclic homology. The first part consists of an excellent exposition of various approaches to string topology and the Chas-Sullivan loop product. The second gives a complete and clear construction of an algebraic model for computing topological cyclic homology. The book provides many ...
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The Heat Kernel Lefschetz Fixed Point Formula for the Spin-C Dirac Operator
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J J Duistermaat
This work uses the heat kernal theory of Berline-Getzler-Vergne to focus on the special case of the spin-c Dirac operators on almost complex manifolds. A large part of the text has a wider scope than spin-c Dirac, such as the asymptotic expansion of heat kernels for generalized Laplace operators.
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Singular Coverings of Toposes
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Marta Bunge, Jonathon Funk, Professor Mario Bunge
This volume presents a fairly self-contained theory of certain singular coverings of toposes, including branched coverings. This is a field that should be of interest to topologists working in knot theory, as well as also to certain categorists. An unusual feature which distinguishes this book from classical treatments of the subject is an ...
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Differential Topology: An Introduction
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by
David B Gauld
This self-contained treatment features 88 helpful illustrations and its subjects include topological spaces and properties, some advanced calculus, differentiable manifolds, orientability, submanifolds and an embedding theorem, and tangent spaces. Additional topics comprise vector fields and integral curves, surgery, classification of orientable ...
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Techniques of Differential Topology in Relativity
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by
Roger Penrose
Acquaints the specialist in relativity theory with some global techniques for the treatment of space-times and will provide the pure mathematician with a way into the subject of general relativity.
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Analysis on Real & Complex Manifolds
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by
Raghavan Narasimhan
Chapter 1 presents theorems on differentiable functions often used in differential topology, such as the implicit function theorem, Sard's theorem and Whitney's approximation theorem. The next chapter is an introduction to real and complex manifolds. It contains an exposition of the theorem of Frobenius, the lemmata of Poincare and Grothendieck ...
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