e99 Online Shopping Mall
Help | |
Home - Pure And Applied Math - General Topology (Books) |
  | Back | 21-40 of 100 | Next 20 |
click price to see details click image to enlarge click link to go to the store
21. Essential Topology (Springer Undergraduate Mathematics Series) by Martin D. Crossley | |
Paperback: 224
Pages
(2005-07-01)
list price: US$39.95 -- used & new: US$30.74 (price subject to change: see help) Asin: 1852337826 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This book brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers prepared and motivated for further study. Written from a thoroughly modern perspective, every topic is introduced with an explanation of why it is being studied, and a huge number of examples provide further motivation. The book is ideal for self-study and assumes only a familiarity with the notion of continuity and basic algebra. Customer Reviews (4)
Best Intro to Topology
Surely not optimal
Best undergraduate topology book
A pleasure to read |
22. Introduction to Set Theory and Topology by Kazimierz Kuratowski | |
Hardcover: 352
Pages
(1972-06)
Isbn: 008016160X Canada | United Kingdom | Germany | France | Japan | |
23. From Geometry to Topology by H. Graham Flegg | |
Paperback: 208
Pages
(2001-09-04)
list price: US$14.95 -- used & new: US$9.35 (price subject to change: see help) Asin: 0486419614 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
Perfect book for the right reader
Easy, but okay...
Very nice and intuitive introducation to topology |
24. Introduction to Topology: Second Edition by Theodore W. Gamelin, Robert Everist Greene | |
Paperback: 256
Pages
(1999-02-16)
list price: US$14.95 -- used & new: US$8.79 (price subject to change: see help) Asin: 0486406806 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (8)
Great book for starters
A Wonderful Book
I'm not good at math
Okay, not great. Overall, I give it a C+
excellent introduction to topology |
25. Introduction to General Topology by K.D. Joshi | |
Hardcover: 424
Pages
(1983-08-24)
-- used & new: US$132.11 (price subject to change: see help) Asin: 0852264445 Canada | United Kingdom | Germany | France | Japan | |
26. The Topology of 4-Manifolds (Lecture Notes in Mathematics / Nankai Institute of Mathematics, Tianjin, P.R. China) by Robion C. Kirby | |
Paperback: 108
Pages
(1989-05-10)
list price: US$26.00 -- used & new: US$20.00 (price subject to change: see help) Asin: 3540511482 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Excellent The author starts the book with an overview of handlebody theory, noting that for the case of interest, 4-dimensional toplogical manifolds must be smooth in order for them to be handlebodies. Smooth handlebody decompositions can be described by Morse theory, and one smooth handlebody decomposition can be related to another via an isotopy of attaching maps and creation or annihilation of handle pairs. The author visualizes handlebodies in four dimensions by drawing their attaching maps in the 3-sphere. This results in the use of framed links to model the attaching maps, with examples of the 3-torus, the Poincare homology 3-sphere, and a homotopy 4-sphere, the latter of which is homeomorphic to the 4-sphere and is a double cover of an exotic smooth structure on 4-d real projective space. The author also gives a brief but interesting discussion on why the methods of this chapter are difficult to do in three dimensions. The theory of intersection forms appears in chapter two, with the author proving first that for a closed, smooth, oriented, 4-d manifold M any element of the second integer homology group is represented by a smoothly imbedded oriented surface. Any two such surfaces can be joined by smooth oriented 3-manifold imbedded in M. The isomorphism between the second homology and cohomology groups (over the integers) modulo torsion is the famous "intersection pairing". The author then proves that two simply-connected, closed, oriented 4-manifolds are homotopy equivalent if and only if their intersection forms are isometric. The proof emphasizes the geometric connection between homotopy type and intersection forms. A brief review of symmetric bilinear forms and characteristic classes is then given, as preparation for the classification results given later in the book. The author treats classification theorems in chapter three, which he describes as deciding which forms, whether symmetric, integral, or unimodular, can be represented by simply connected closed 4-manifolds. The relation between forms and homotopy type makes this implicitly a classification for the homotopy type of the manifold. Rohlin's theorem was historically the first major result in this problem, but the author delays its proof until chapter eleven. The author briefly discusses the work of Freedman in the topological case, and Donaldson, in the smooth case. Spin structures are discussed in chapter four and several examples are given. The author also shows how to relate spin structures on the boundary of a manifold to spin structures on the manifold itself, to set up later discussions on cobordism. Chapter five then concentrates on the Lie group spin structure of the 3-torus T3(Lie) and the surface constructed by taking the nine-fold direct sum of complex 2-d projective space and its reverse orientation. The latter is a complex analytic projection, which is a smooth fiber bundle with fiber the two-torus except for a finite number of singular fibers. The author shows in detail how to use this object to obtain a spin manifold with spin boundary T3(Lie). Chapter six is devoted to showing how to immerse closed, smooth, oriented 4-manifolds in Euclidean 6-d space. This involves the calculation of a characteristic class in the second integral cohomology group. Then as a warm-up to showing that a spin 4-manifold with index zero spin bounds a spin 5-manifold, the author proves in chapter 7 that every orientable 3-manifold is spin, bounds an orientable 4-manifold, and if spin bounds a spin 4-manifold with only 0-handles. In chapter eight, the author proves that a closed, smooth, connected, and orientable 4-manifold is the boundary of a smooth 5-manifold if the first Pontryagin class is 0. If the 4-manifold is spin, and the first Pontryagin class is 0, then there exists a smooth, spin 5-manifold whose boundary is the 4-manifold, where both manifolds are considered as spin manifolds. Chapter nine proves the Hirzebruch index theorem in dimension 4, and the author shows that the cobordism ring for SO and Spin is the integers. Chapter ten is devoted to a proof of Wall's theorem and the h-cobordism theorem in dimension 4. The geometric proof of Rohlin's theorem promised by the author is finally done in chapter eleven. Casson handles, so important in the proof of the 4-d Poincare conjecture, are discussed in chapter twelve. The author shows the role of the Whitney trick in dimensions 5 or more, and how its failure in dimension 4 results in the use of Casson handles, which are constructed using the famous "finger moves". He gives an explicit handlebody description of the simplest Casson handle, and then relates it to the Whitehead continuum. The most fascinating part of the book is chapter thirteen, which outlines briefly Freedman's proof of the 4-dimensional Poincare conjecture. The proof makes use of 4-dimensional handlebody theory and decomposition space theory. Casson handles are decomposed via an imbedding of a Cantor set of Casson handles inside them. The "Big Reimbedding theorem" of Freedman, which points to the existence of an exotic smooth structure on the 3-sphere cross the real line, is quoted but not proved. The book ends with chapter fourteen being a brief discussion of exotic structures, their existence following from the non-smoothness of Casson handles. ... Read more |
27. Schaum's Outline Series Theory and Problems of General Topology by Seymour Lipschutz | |
Paperback:
Pages
(1965-01-01)
-- used & new: US$10.00 (price subject to change: see help) Asin: B000GR4P3K Canada | United Kingdom | Germany | France | Japan | |
28. Algebraic Topology by William Fulton | |
Paperback: 430
Pages
(1995-07-27)
list price: US$49.95 -- used & new: US$32.00 (price subject to change: see help) Asin: 0387943277 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description The first part of the book emphasizes relations with calculus and uses these ideas to prove the Jordan curve theorem. The study of fundamental groups and covering spaces emphasizes group actions. A final section gives a taste of the generalization to higher dimensions. Customer Reviews (3)
A book of ideas As a warm-up in Part 1, the author gives an overview of calculus in the plane, with the intent of eventually defining the local degree of a mapping from an open set in the plane to another. This is done in the second part of the book, where winding numbers are defined, and the important concept of homotopy is introduced. These concepts are shown to give the fundamental theorem of algebra and invariance of dimension for open sets in the plane. The delightful Ham-Sandwich theorem is discussed along with a proof of the Lusternik-Schnirelman-Borsuk theorem. I would like to see a constructive proof of this theorem, but I do not know of one. Part 3 is the tour de force of algebraic topology, for it covers the concepts of cohomology and homology. The author pursues a non-traditional approach to these ideas, since he introduces cohomology first, via the De Rham cohomology groups, and these are used to proved the Jordan curve theorem. Homology is then effectively introduced via chains, which is a much better approach than to hit the reader with a HOM functor.Part 4 discusses vector fields and the discussion reads more like a textbook in differential topology with the emphasis on critical points, Hessians, and vector fields on spheres. This leads naturally to a proof of the Euler characteristic. The Mayer-Vietoris theory follows in Part 5, for homology first and then for cohomology. The fundamental group finally makes its appearance in Part 6 and 7, and related to the first homology group and covering spaces. The author motivates nicely the Van Kampen theorem. A most interesting discussion is in part 8, which introduces Cech cohomology. The author's treatment is the best I have seen in the literature at this level. This is followed by an elementary overview of orientation using Cech cocycles. All of the constructions done so far in the plane are generalized to surfaces in Part 9. Compact oriented surfaces are classified and the second de Rham cohomology is defined, which allows the proof of the full Mayer-Vietoris theorem. The most important part of the book is Part 10, which deals with Riemann surfaces. The author's treatment here is more advanced than the rest of the book, but it is still a very readable discussion. Algebraic curves are introduced as well as a short discussion of elliptic and hyperelliptic curves. The level of abstraction increases greatly in the last part of the book, where the results are extended to higher dimensions. Homological algebra and its ubiquitous diagram chasing are finally brought in, but the treatment is still at a very understandable level. For examples of the author's pedagogical ability, I recommend his book Toric Varieties, and his masterpiece Intersection Theory.
This is one of the great algebraic topology books!
Probably better as a 2nd (or 3rd) course rather than 1st |
29. Euler's Gem: The Polyhedron Formula and the Birth of Topology by David S. Richeson | |
Hardcover: 332
Pages
(2008-09-08)
list price: US$27.95 -- used & new: US$10.77 (price subject to change: see help) Asin: 0691126771 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (12)
Topology Starter Book
This book is a real gem itself
Very Good, But Challenging
A Gem Indeed!
A gem of mathematical results produced by one of the masters of mathematics |
30. History of Topology | |
Hardcover: 1068
Pages
(2006-03-13)
list price: US$317.00 -- used & new: US$317.00 (price subject to change: see help) Asin: 0444823751 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
A lot of very good essays
Absolutely Brilliant No home should be without one. ... Read more |
31. 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 |
32. Differential Forms in Algebraic Topology (Graduate Texts in Mathematics) by Raoul Bott, Loring W. Tu | |
Paperback: 350
Pages
(2010-11-02)
list price: US$74.95 -- used & new: US$60.14 (price subject to change: see help) Asin: 1441928154 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (7)
a masterpiece of exposition
So far so good
good book
wonderfully clear, useful book
A unique mathematics book That makes this one of my all time favourite mathematics texts. ... Read more |
33. Topology and Geometry (Graduate Texts in Mathematics) by Glen E. Bredon | |
Paperback: 557
Pages
(2010-11-02)
list price: US$79.95 -- used & new: US$64.09 (price subject to change: see help) Asin: 1441931031 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS Customer Reviews (7)
never really liked it
a different perspective
excellent for first year graduate study
Among the best textbooks in algebraic topology.
The Graduate Sudent's Topology Bible |
34. General Topology by John L. Kelley | |
Hardcover:
Pages
Asin: B000VLBE44 Canada | United Kingdom | Germany | France | Japan | |
35. Algorithmic Topology and Classification of 3-Manifolds (Algorithms and Computation in Mathematics) by Sergei Matveev | |
Paperback: 492
Pages
(2010-11-02)
list price: US$89.95 -- used & new: US$80.96 (price subject to change: see help) Asin: 3642079601 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description From the reviews of the 1st edition: "This book provides a comprehensive and detailed account of different topics in algorithmic 3-dimensional topology, culminating with the recognition procedure for Haken manifolds and including the up-to-date results in computer enumeration of 3-manifolds. Originating from lecture notes of various courses given by the author over a decade, the book is intended to combine the pedagogical approach of a graduate textbook (without exercises) with the completeness and reliability of a research monograph… All the material, with few exceptions, is presented from the peculiar point of view of special polyhedra and special spines of 3-manifolds. This choice contributes to keep the level of the exposition really elementary. In conclusion, the reviewer subscribes to the quotation from the back cover: "the book fills a gap in the existing literature and will become a standard reference for algorithmic 3-dimensional topology both for graduate students and researchers". Zentralblatt für Mathematik 2004 For this 2nd edition, new results, new proofs, and commentaries for a better orientation of the reader have been added. In particular, in Chapter 7 several new sections concerning applications of the computer program "3-Manifold Recognizer" have been included. |
36. A History of Algebraic and Differential Topology, 1900 - 1960 (Modern Birkhäuser Classics) by Jean Dieudonné | |
Paperback: 648
Pages
(2009-06-09)
list price: US$69.95 -- used & new: US$55.67 (price subject to change: see help) Asin: 0817649069 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description 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 Customer Reviews (1)
More than a mere "history". |
37. Differential Topology and General Equilibrium with Complete and Incomplete Markets by Antonio Villanacci, Laura Carosi, Pierluigi Benevieri, Andrea Battinelli | |
Paperback: 512
Pages
(2010-11-02)
list price: US$199.00 -- used & new: US$157.99 (price subject to change: see help) Asin: 144195306X Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
38. An introduction to general topology (Merrill mathematics series) by Paul E Long | |
Unknown Binding: 281
Pages
(1971)
-- used & new: US$19.00 (price subject to change: see help) Asin: 0675092531 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
39. Fundamentals of General Topology: Problems and Exercises (Mathematics and Its Applications) by A.V. Arkhangel'skii, V.I. Ponomarev | |
Paperback: 436
Pages
(2001-11-30)
list price: US$129.00 -- used & new: US$102.47 (price subject to change: see help) Asin: 1402003080 Canada | United Kingdom | Germany | France | Japan | |
40. Foundations of general topology (International series of monographs on pure and applied mathematics) by AÌkos CsaÌszaÌr | |
Hardcover: 380
Pages
(1963)
Asin: B0007IT8GC Canada | United Kingdom | Germany | France | Japan | |
  | Back | 21-40 of 100 | Next 20 |