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41. Hodge Theory and Complex Algebraic Geometry I: Volume 1 (Cambridge Studies in Advanced Mathematics) (v. 1) by Claire Voisin | |
Paperback: 332
Pages
(2008-02-04)
list price: US$46.99 -- used & new: US$37.92 (price subject to change: see help) Asin: 0521718015 Canada | United Kingdom | Germany | France | Japan | |
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42. 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 | |
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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. |
43. 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 | |
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My First Book in Topology
$35 - This book is FREE online!
Elegant introduction to topology. |
44. Applications of Algebraic Topology: Graphs and Networks, The Picard-Lefschetz Theory and Feynman Integrals (Applied Mathematical Sciences 16) (Volume 0) by S. Lefschetz | |
Paperback: 189
Pages
(1975-05-13)
list price: US$27.00 -- used & new: US$18.75 (price subject to change: see help) Asin: 038790137X Canada | United Kingdom | Germany | France | Japan | |
45. Fundamental Algebraic Geometry (Mathematical Surveys and Monographs) by Barbara Fantechi, Lothar Gottsche, Luc Illusie, Steven L. Kleiman, Nitin Nitsure | |
Paperback: 339
Pages
(2006-12-10)
list price: US$79.00 -- used & new: US$79.00 (price subject to change: see help) Asin: 0821842455 Canada | United Kingdom | Germany | France | Japan | |
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46. Topological Methods in Algebraic Geometry (Classics in Mathematics) by Friedrich Hirzebruch | |
Paperback: 234
Pages
(1995-02-24)
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47. Probabilities on Algebraic Structures (Dover Books on Mathematics) by Ulf Grenander | |
Paperback: 224
Pages
(2008-02-04)
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48. Directed Algebraic Topology: Models of Non-Reversible Worlds (New Mathematical Monographs) by Marco Grandis | |
Hardcover: 444
Pages
(2009-10-30)
list price: US$95.00 -- used & new: US$65.00 (price subject to change: see help) Asin: 0521760364 Canada | United Kingdom | Germany | France | Japan | |
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49. 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. |
50. Algebraic K-Theory II. . "Classical" Algebraic K-Theory, and Connections with Arithmetic.(Lecture Notes in Mathematics 342) (Volume 0) by Hyman Bass | |
Paperback: 527
Pages
(1973-01-01)
list price: US$59.00 -- used & new: US$50.09 (price subject to change: see help) Asin: 3540064354 Canada | United Kingdom | Germany | France | Japan | |
51. Essentials of Topology with Applications (Textbooks in Mathematics) by Steven G. Krantz | |
Hardcover: 420
Pages
(2009-07-28)
list price: US$89.95 -- used & new: US$58.00 (price subject to change: see help) Asin: 1420089749 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Brings Readers Up to Speed in This Important and Rapidly Growing Area Supported by many examples in mathematics, physics, economics, engineering, and other disciplines, Essentials of Topology with Applications provides a clear, insightful, and thorough introduction to the basics of modern topology. It presents the traditional concepts of topological space, open and closed sets, separation axioms, and more, along with applications of the ideas in Morse, manifold, homotopy, and homology theories. After discussing the key ideas of topology, the author examines the more advanced topics of algebraic topology and manifold theory. He also explores meaningful applications in a number of areas, including the traveling salesman problem, digital imaging, mathematical economics, and dynamical systems. The appendices offer background material on logic, set theory, the properties of real numbers, the axiom of choice, and basic algebraic structures. Taking a fresh and accessible approach to a venerable subject, this text provides excellent representations of topological ideas. It forms the foundation for further mathematical study in real analysis, abstract algebra, and beyond. Customer Reviews (1)
Poorly conceived and executed |
52. Fourier-Mukai Transforms in Algebraic Geometry (Oxford Mathematical Monographs) by Daniel Huybrechts | |
Hardcover: 280
Pages
(2006-06-29)
list price: US$125.00 -- used & new: US$107.85 (price subject to change: see help) Asin: 0199296863 Canada | United Kingdom | Germany | France | Japan | |
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53. Intuitive Combinatorial Topology (Universitext) by V.G. Boltyanskii, V.A. Efremovich | |
Paperback: 141
Pages
(2010-11-02)
list price: US$64.95 -- used & new: US$54.47 (price subject to change: see help) Asin: 1441928820 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
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Gentle topology book without heart |
54. Topology, Ergodic Theory, Real Algebraic Geometry | |
Hardcover: 286
Pages
(2001-05-01)
list price: US$131.00 -- used & new: US$127.00 (price subject to change: see help) Asin: 0821827405 Canada | United Kingdom | Germany | France | Japan | |
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55. Geometry and Topology of Configuration Spaces by Edward R. Fadell, Sufian Y. Husseini | |
Hardcover: 308
Pages
(2000-12-28)
list price: US$169.00 -- used & new: US$74.87 (price subject to change: see help) Asin: 3540666699 Canada | United Kingdom | Germany | France | Japan | |
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56. Algebra, Algebraic Topology and their Interactions: Proceedings of a Conference held in Stockholm, Aug. 3 - 13, 1983, and later developments (Lecture Notes in Mathematics) | |
Paperback: 416
Pages
(1986-04-24)
list price: US$46.00 -- used & new: US$14.98 (price subject to change: see help) Asin: 3540164537 Canada | United Kingdom | Germany | France | Japan | |
57. Algebraic Topology and Algebraic K-Theory: Proceedings of a Symposium in Honor of John C. Moore. (AM-113) (Annals of Mathematics Studies) | |
Paperback: 567
Pages
(1987-11-01)
list price: US$92.50 -- used & new: US$32.50 (price subject to change: see help) Asin: 0691084262 Canada | United Kingdom | Germany | France | Japan | |
58. Boundedly Controlled Topology: Foundations of Algebraic Topology and Simple Homotopy Theory (Lecture Notes in Mathematics) by Douglas R. Anderson, Hans J. Munkholm | |
Paperback: 309
Pages
(1988-07-22)
list price: US$46.00 -- used & new: US$38.19 (price subject to change: see help) Asin: 3540193979 Canada | United Kingdom | Germany | France | Japan | |
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59. Lectures on Algebraic and Differential Topology: Delivered at the 2. ELAM (Lecture Notes in Mathematics) by R. Bott, S. Gitler | |
Paperback: 184
Pages
(1972-09-20)
list price: US$26.00 -- used & new: US$22.31 (price subject to change: see help) Asin: 354005944X Canada | United Kingdom | Germany | France | Japan | |
60. Higher Algebraic K-Theory: An Overview (Lecture Notes in Mathematics) by Emilio Lluis-Puebla, Jean-Louis Loday, Henri Gillet, Christophe Soule, Victor Snaith | |
Paperback: 164
Pages
(1993-01-26)
list price: US$37.00 -- used & new: US$31.65 (price subject to change: see help) Asin: 3540550070 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
A quick overview of a highly developed branch of mathematics This book goes considerably further then these relatively elementary considerations, in that it treats the higher K-groups and the connection with topological K-theory. Readers will need an extensive background in algebra and topology to appreciate the constructions in this book, which are mostly formal and thus there is the canonical inverse relationship between rigor and understanding. There are many places in the book though where readers can gain useful insights into a mature and highly developed branch of mathematics. As was hinted above, for a ring R, K0 gives a measure of the failure of finitely generated projective R-modules from having a dimension theory like that of vector spaces.The first algebraic K-group K1 of a ring R is the quotient group of the infinite general linear group GL(R) modulo the infinite elementary group E(R) (the infinite elementary group comes from considering those matrices which differ from the identity only by an off diagonal element). Whitehead's Lemma shows that E(R) is a normal subgroup of GL(R). One can show that K1 of the integers is just {-1, 1}, and, for more general commutative rings R, that the determinant on GL(R) to the units R* of R induces a universal homomorphism and K1(R) is equal to these units. Thus the determinant gives in this case a universal invariant as was noted above. The second algebraic K-group of a ring R is then defined by generalizing the elementary group to the `Steinberg group' and then taking limits. There is an epimorphism from the Steinberg group to the elementary group and after passing to the infinite limit, the kernel of this epimorphism is defined as the second algebraic K-group of the ring R. K2(R) measures to what extent the Steinberg relations do not define the relations for the elementary group. One can show that K2 of the integers Z is Z/2, and that K2 of the direct product of two rings is the direct sum of their K2 groups. Topological K-theory, also discussed in detail throughout the book, has its origins in the theory of vector bundles. Two vector bundles are called `stably-equivalent' if they are isomorphic after taking their direct sum with trivial bundles. Stable equivalence forms an equivalence relation and the stable classes form a ring under direct sum and tensor product. This ring is called the K-ring K(X) of the space X on which the vector bundles are defined. If X is compact and E is a vector bundle over X, then the sheaf of sections of this vector bundle is a finitely generated projective module over the ring C(X) of continuous functions on X. This result is known as the Serre-Swan theorem and allows one to discuss the K-theory of the space X in terms of the K-theory of C(X). The properties of this K-theory satisfy those needed to make it a cohomology theory, except for the dimension axiom. Topological K-theory also has the property of Bott periodicity, wherein the K-groups at one dimension are isomorphic to those of two dimensions less. The higher topological K-theory groups have a counterpart in algebraic K-theory. This can be shown in several different ways, but this book discusses the Quillen or `Q-construction' of higher algebraic K-theory. Dependent on the notion of a `nerve' of a category and its classifying space, the Q-construction involves starting with an exact category M and defining a new category QM with the same objects but with morphisms satisfying certain properties of admissibility and composition. For a small exact category M, the ith higher algebraic K-group of this category is defined as the (i+1)-th homotopy group of the classifying space of M. The book also discusses, for a ring R, the `+-construction' of Quillen, which was the first definition of higher algebraic K-theory, and is considerably less esoteric than the Q-construction since it involves the well-known result that GL(R) is the first homotopy group of the classifying space of GL(R) and the intuitive geometric construction of adding cells to the classifying space to form a new space that has certain useful properties. The ith-higher algebraic K-group is then defined as the ith-homotopy group of this space. Although it is not done in this book, this definition coincides with the Q-construction when the latter is applied to the category of finitely generated projective R-modules. ... Read more |
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