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61. A First Course in Geometric Topology and Differential Geometry by Ethan D. Bloch | |
Hardcover: 440
Pages
(1996-12-01)
list price: US$89.95 -- used & new: US$62.97 (price subject to change: see help) Asin: 0817638407 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (5)
Great Book
a remark on omissions
Good introduction After a brief overview of the elementary topology of subsets of Euclidean space in chapter 1, topological surfaces are discussed in chapter 2. Surfaces are built up from arcs, disks, and one-spheres. Unfortunately, the proofs of the theorem of invariance of domain and the Schonflies Theorem are not included, but references are given. Gluing techniques though are effectively discussed, and the author does not hesitate to use diagrams to explain the relevant concepts. The more popular constructions in surface topology, namely the Mobius strip and the Klein bottle are given as examples of the cutting and pasting techniques. The amusing fact that the Klein bottle can be obtained from gluing two Mobius strips along their boundaries is proven. The theory of simplicial surfaces is discussed in the next chapter. Simplicial surfaces are much easier to deal with for beginning students of topology. Simplicial complexes are introduced first, and the author then studies which simplicial complexes have underlying spaces that are topological surfaces. He proves that this is the case when each one-dimensional simplex of the complex is the face of precisely two two-dimensional simplices, and the underlying space of each link of each zero-dimensional simplex of the complex is a one-dimensional sphere. Unfortunately, the author does not prove that any compact topological surface in n-dimensional Euclidean space can be triangulated. The Euler characteristic is defined first for 2-complexes and it is shown that it is the same for two simplicial surfaces that triangulate a compact topological surface. The author does prove in detail the classification of compact connected surfaces. Interestingly, the author also proves a simplicial analogue of the Gauss-Bonnet theorem, and gives a proof of the Brouwer fixed point theorem. The author turns to smooth surfaces in the next few chapters, wherein curves are defined along with the relevant differential-geometric notions such as curvature and torsion. The fundamental theorem of curves is proven. The reader is first introduced to the concept of what in more advanced treatments is called a differentiable manifold, and several concrete examples are given of smooth surfaces. The differential geometry of smooth surfaces is outlined, with the first fundamental form and directional derivatives discussed in great detail. The reader should be familiar with the inverse function theorem to appreciate the discussion of regular values. Even more interesting differential geometry is discussed in chapter 6, which covers the curvature of smooth surfaces. The important Gauss map is defined, along with the Weingarten map and the second fundamental form. This allows an intrinsic notion of curvature, but the author does perform explicit computations of curvature using various choices of coordinates. The proof that Gaussian curvature is intrinsic (Theorema Egregium) is proven, along with the fundamental theorem of surfaces. Geodesics, so important in physical applications, are discussed in the next chapter. The reader gets a first look at the "Christoffel symbols", even though they are not designated as such in the book. The book ends with a thorough treatment of the Gauss-Bonnet theorem for smooth surfaces. The smooth case is much more difficult to prove than the simplicial case, as the reader will find out when studying this chapter. The author also gives a very brief introduction to non-Euclidean geometry.
Presentation of The Spirit...
Just a mediocre book of lesser extent |
62. Introduction to Differential Topology by T. Bröcker, K. Jänich | |
Paperback: 172
Pages
(1982-10-29)
list price: US$40.99 -- used & new: US$32.96 (price subject to change: see help) Asin: 0521284708 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Excellent graduate-level introduction, slightly marred by poor editing & translation |
63. Differential Geometry and Topology: With a View to Dynamical Systems (Studies in Advanced Mathematics) by Keith Burns, Marian Gidea | |
Hardcover: 400
Pages
(2005-05-27)
list price: US$99.95 -- used & new: US$69.97 (price subject to change: see help) Asin: 1584882530 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, and integration on manifolds provide the foundation for many applications in dynamical systems and mechanics. The authors also discuss the Gauss-Bonnet theorem and its implications in non-Euclidean geometry models. The differential topology aspect of the book centers on classical, transversality theory, Sard's theorem, intersection theory, and fixed-point theorems. The construction of the de Rham cohomology builds further arguments for the strong connection between the differential structure and the topological structure. It also furnishes some of the tools necessary for a complete understanding of the Morse theory. These discussions are followed by an introduction to the theory of hyperbolic systems, with emphasis on the quintessential role of the geodesic flow. The integration of geometric theory, topological theory, and concrete applications to dynamical systems set this book apart. With clean, clear prose and effective examples, the authors' intuitive approach creates a treatment that is comprehensible to relative beginners, yet rigorous enough for those with more background and experience in the field. Customer Reviews (2)
Excellent book
A very good book |
64. Introduction to Symplectic Topology (Oxford Mathematical Monographs) by Dusa McDuff, Dietmar Salamon | |
Paperback: 496
Pages
(1999-07-29)
list price: US$125.00 -- used & new: US$104.27 (price subject to change: see help) Asin: 0198504519 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Perfect
A must for researchers new to the field The discussion begins with classic topology and cover a variety offinal year undergraduate topics such as complex manifolds and inversedifferential techniques before moving into the vastly complex world ofSymplectic Topology. A must for researchers new to the field ... Read more |
65. Topology and Groupoids by Ronald Brown | |
Paperback: 538
Pages
(2006-02-24)
list price: US$31.99 -- used & new: US$22.00 (price subject to change: see help) Asin: 1419627228 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Topology and Groupoids - great value!! |
66. An Introduction to Algebraic Topology (Graduate Texts in Mathematics) by Joseph J. Rotman | |
Hardcover: 460
Pages
(1988-08-17)
list price: US$84.95 -- used & new: US$52.68 (price subject to change: see help) Asin: 0387966781 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
A readable alternative to Hatcher
Rotman does it again.
Good textbook |
67. A Combinatorial Introduction to Topology by Michael Henle | |
Paperback: 310
Pages
(1994-03-14)
list price: US$14.95 -- used & new: US$8.95 (price subject to change: see help) Asin: 0486679667 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (7)
A reader's opinion
A good start Combinatorial topology can be viewed first as an attempt to study the properties of polyhedra and how they fit together to form more complicated objects. Conversely, one can view it as a way of studying complicated objects by breaking them up into elementary polyhedral pieces. The author takes the former view in this book, and he restricts his attention to the study of objects that are built up from polygons, with the proviso that vertices are joined to vertices and (whole) edges are joined to (whole) edges. He begins the book with a consideration of the Euler formula, and as one example considers the Euler number of the Platonic solids, resulting in a Diophantine equation. This equation only has five solutions, the Platonic solids. The author then motivates the concept of a homeomorphism (he calls them "topological equivalences") by considering topological transformations in the plane. Using the notion of topological equivalence he defines the notions of cell, path, and Jordan curve. Compactness and connectedness are then defined, along with the general notion of a topological space. Elementary notions from differential topology are then considered in chapter 2, with the reader encountering for the first time the connections between analysis and topology, via the consideration of the phase portraits of differential equations. Brouwer's fixed point theorem is proved via Sperner's lemma, the latter being a combinatorial result which deals with the labeling of vertices in a triangulation of the cell. Gradient vector fields, the Poincare index theorem, and dual vector fields,which are some elementary notions in Morse theory, are treated here briefly. An excellent introduction to some elementary notions from algebraic topology is done in chapter 3. The author treats the case of plane homology (mod 2), which is discussed via the use of polygonal chains on a grating in the plane. Beginning students will find the presentation very understandable, and the formalism that is developed is used to give a proof of the Jordan curve theorem. Then in chapter 4, the author proves the classification theorem for surfaces, using a combinatorial definition of a surface. The author raises the level of complication in chapter 5, wherein he studies the (mod 2) homology of complexes. A complex is defined somewhat loosely as a topological space that is constructed out of vertices, edges, and polygons via topological identification. He proves the invariance theorem for triangulations of surfaces by showing that the homology groups of the triangulation are same as the homology groups of the plane model of the surface. This is an example of the invariance principle, and the author briefly details some of the history of invariance principles, such as the Hauptvermutung, its counterexample due to the mathematician John Milnor, and Heawood's conjecture, the latter of which deals with the minimum number of colors needed to color all maps on a surface with a given Euler characteristic. Integral homology is also introduced by the author, and he shows the origin of torsion in the consideration of the "twist" in a surface. In the last part of the book, the author returns to the consideration of continuous transformations, tackling first the idea of a universal covering space. Algebraic topology again makes its appearance via the consideration of transformations of triangulated topological spaces, i.e. simplicial transformations. He shows how these transformations induce transformations in the homology groups, thus introducing the reader to some notions from category theory. The elaboration of the invariance theorem for homology leads the author to studying the properties of the group homomorphisms via matrix algebra, and then to a proof of the Lefschetz fixed point theorem. The book ends with a brief discussion of homotopy, topological dynamics, and alternative homology theories. The beginning student of topology will thus be well prepared to move on to more rigorous and advanced treatments of differential, algebraic, and geometric topology after the reading of this book. There are still many unsolved problems in these areas, and each one of these will require a deep understanding and intuition of the underlying concepts in topology. This book is a good start.
Splendidly intuitive yet rigorous There are excellent examples, clear writing, and humour. An outstanding introduction. One nice feature is that he bases his notions of continuity on "nearness" not epsilon-delta.
An excellent read
Not for resolute students of algebraci/diff. topology. |
68. Elementary Topology by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, and V. M. Kharlamov | |
Hardcover: 400
Pages
(2008-09-17)
list price: US$59.00 -- used & new: US$39.70 (price subject to change: see help) Asin: 0821845063 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
good concept, too many typos |
69. Invitations to Geometry and Topology (Oxford Graduate Texts in Mathematics, 7) | |
Hardcover: 338
Pages
(2003-01-02)
list price: US$115.00 -- used & new: US$90.75 (price subject to change: see help) Asin: 0198507720 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
70. Topology of Foliations: An Introduction (Translations of Mathematical Monographs) by Itiro Tamura | |
Paperback: 193
Pages
(2006-09-08)
list price: US$80.00 -- used & new: US$53.61 (price subject to change: see help) Asin: 0821842005 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
71. Analytic Topology (Colloquium Publications) by G. T. Whyburn | |
Paperback: 280
Pages
(1942-12-31)
list price: US$54.00 -- used & new: US$57.62 (price subject to change: see help) Asin: 0821810286 Canada | United Kingdom | Germany | France | Japan | |
72. The General Topology of Dynamical Systems (Graduate Studies in the Mathematical Sciences, V. 1) by Ethan Akin | |
Hardcover: 261
Pages
(1993-03-29)
list price: US$42.00 -- used & new: US$76.08 (price subject to change: see help) Asin: 0821838008 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
73. Topology: An Introduction with Application to Topological Groups (Phoenix Edition) by George McCarty | |
Hardcover: 288
Pages
(2006-01-03)
list price: US$49.50 -- used & new: US$17.82 (price subject to change: see help) Asin: 0486450821 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
I just couldn't read this.
Excellent for Self-Teaching
An oldy but a goody May not work well for a one-semester course, as the topology and group theory are interwoven fairly substantially.One does not need to know group theory before reading the book, but one cannot easily escape it and still get at all the topology. ... Read more |
74. Foundations of General Topology by W.J. Pervin | |
Hardcover:
Pages
(1964-12)
list price: US$12.95 Isbn: 0125509502 Canada | United Kingdom | Germany | France | Japan | |
75. Lectures on Algebraic Topology (Classics in Mathematics) by Albrecht Dold, A. Dold | |
Paperback: 400
Pages
(1995-02-15)
list price: US$59.95 -- used & new: US$44.00 (price subject to change: see help) Asin: 3540586601 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Singular homology, products and manifolds
Elgant treatment of homology theory. |
76. Algebraic and Differential Topology (Classics of Soviet Mathematics) by R. V. Gamkrelidze | |
Hardcover: 252
Pages
(1987-03-06)
list price: US$129.95 -- used & new: US$111.20 (price subject to change: see help) Asin: 2881240356 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
77. Topology and Geometry in Physics (Lecture Notes in Physics) | |
Paperback: 360
Pages
(2009-12-15)
list price: US$99.00 -- used & new: US$89.10 (price subject to change: see help) Asin: 3642062091 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Application of the concepts and methods of topology and geometry have led to a deeper understanding of many crucial aspects in condensed matter physics, cosmology, gravity and particle physics. This book can be considered an advanced textbook on modern applications and recent developments in these fields of physical research. Written as a set of largely self-contained extensive lectures, the book gives an introduction to topological concepts in gauge theories, BRST quantization, chiral anomalies, sypersymmetric solitons and noncommutative geometry. It will be of benefit to postgraduate students, educating newcomers to the field and lecturers looking for advanced material. |
78. Elementary Differential Topology. (AM-54) (Annals of Mathematics Studies) by James R. Munkres | |
Paperback: 112
Pages
(1966-12-31)
list price: US$37.50 -- used & new: US$26.19 (price subject to change: see help) Asin: 0691090939 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Customer Reviews (1)
few topics, of very limited value |
79. A First Course in Topology: Continuity and Dimension (Student Mathematical Library) by John McCleary | |
Paperback: 210
Pages
(2006-04-07)
list price: US$35.00 -- used & new: US$29.92 (price subject to change: see help) Asin: 0821838849 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
My First Book in Topology
$35 - This book is FREE online!
Elegant introduction to topology. |
80. Protein Geometry, Classification, Topology and Symmetry: A Computational Analysis of Structure (Series in Biophysics) by William R. Taylor, Andras Aszodi | |
Hardcover: 348
Pages
(2004-10-01)
list price: US$98.95 -- used & new: US$79.16 (price subject to change: see help) Asin: 0750309857 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
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