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21. Differentiable Manifolds (Modern Birkhäuser Classics) by Lawrence Conlon | |
Paperback: 418
Pages
(2008-01-11)
list price: US$44.95 -- used & new: US$28.00 (price subject to change: see help) Asin: 081764766X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description The basics of differentiable manifolds, global calculus, differential geometry, and related topics constitute a core of information essential for the first or second year graduate student preparing for advanced courses and seminars in differential topology and geometry. Differentiable Manifolds is a text designed to cover this material in a careful and sufficiently detailed manner, presupposing only a good foundation in general topology, calculus, and modern algebra. This second edition contains a significant amount of new material, which, in addition to classroom use, will make it a useful reference text. Topics that can be omitted safely in a first course are clearly marked, making this edition easier to use for such a course, as well as for private study by non-specialists. Customer Reviews (1)
Couldn't be better! I'll bow down on this one !!!!! |
22. The Wild World of 4-Manifolds by Alexandru Scorpan | |
Hardcover: 609
Pages
(2005-05-10)
list price: US$72.00 -- used & new: US$68.00 (price subject to change: see help) Asin: 0821837494 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description -- Robion C. Kirby, University of California Berkeley This is a panorama of the topology of simply-connected smooth manifolds of dimension four. Dimension four is unlike any other dimension; it is large enough to have room for wild things to happen, but too small to have room to undo them. For example, only manifolds of dimension four can exhibit infinitely many distinct smooth structures. Indeed, their topology remains the least understood today. The first part of the book puts things in context with a survey of higher dimensions and of topological 4-manifolds. The second part investigates the main invariant of a 4-manifold--the intersection form--and its interaction with the topology of the manifold. The third part reviews complex surfaces as an important source of examples. The fourth and final part of the book presents gauge theory. This differential-geometric method has brought to light the unwieldy nature of smooth 4-manifolds; and although the method brings new insights, it has raised more questions than answers. The structure of the book is modular and organized into a main track of approximately 200 pages, which are augmented with copious notes at the end of each chapter, presenting many extra details, proofs, and developments. To help the reader, the text is peppered with over 250 illustrations and has an extensive index. Customer Reviews (1)
best simultaneous introduction to both topological and smooth 4-manifolds |
23. An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised, Volume 120, Second Edition (Pure and Applied Mathematics) by William M. Boothby | |
Paperback: 400
Pages
(2002-08-19)
list price: US$112.00 -- used & new: US$91.51 (price subject to change: see help) Asin: 0121160513 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (5)
Great book
This is a book for REAL mathematicians
When accountants and soldiers take interest in geometry.....
great introductory text
Very Nice Nontrivial Introduction The book does a good job at stimulating those studying it to developintuition. I found the book helpful when I was first studying the subject. ... Read more |
24. Osserman Manifolds in Semi-Riemannian Geometry (Lecture Notes in Mathematics) by Eduardo Garcia-Rio, Demir N. Kupeli, Ramon Vazquez-Lorenzo | |
Paperback: 178
Pages
(2002-03-22)
list price: US$39.00 -- used & new: US$31.76 (price subject to change: see help) Asin: 3540431446 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
25. Metric Rigidity Theorems on Hermitian Locally Symmetric Manifolds (Series in Pure Mathematics, V. 6) by Ngaiming Mok | |
Hardcover: 278
Pages
(1989-03)
list price: US$82.00 -- used & new: US$82.00 (price subject to change: see help) Asin: 9971508001 Canada | United Kingdom | Germany | France | Japan | |
26. Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88) (Annals of Mathematics Studies) by Robion C. Kirby, Laurence C. Siebenmann | |
Paperback: 368
Pages
(1977-05-01)
list price: US$75.00 -- used & new: US$61.00 (price subject to change: see help) Asin: 0691081913 Canada | United Kingdom | Germany | France | Japan | |
27. Foundations of Differentiable Manifolds and Lie Groups (Graduate Texts in Mathematics) by Frank W. Warner | |
Paperback: 292
Pages
(2010-11-02)
list price: US$74.95 -- used & new: US$60.14 (price subject to change: see help) Asin: 1441928200 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds. The book also provides a proof of the de Rham theorem via sheaf cohomology theory and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem. Customer Reviews (5)
Worthless
Great book, but not perfect or ideal for every purpose
Don'twaste your money
Good, as long as you have enough background
A good book if you have some background |
28. Manifolds and Differential Geometry (Graduate Studies in Mathematics) by Jeffrey M. Lee | |
Hardcover: 671
Pages
(2009-11-25)
list price: US$89.00 -- used & new: US$89.00 (price subject to change: see help) Asin: 0821848151 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
FINALLY, AN EXCELLENT BOOK IN MODERN DIFFERENTIAL GEOMETRY! |
29. Differential Geometry and Analysis on CR Manifolds (Progress in Mathematics) by Sorin Dragomir, Giuseppe Tomassini | |
Hardcover: 487
Pages
(2006-03-17)
list price: US$134.00 -- used & new: US$41.04 (price subject to change: see help) Asin: 0817643885 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description The study of CR manifolds lies at the intersection of three main mathematical disciplines: partial differential equations, complex analysis in several complex variables, and differential geometry. While the PDE and complex analytic aspects have been intensely studied in the last fifty years, much effort has recently been made to understand the differential geometric side of the subject. This monograph provides a unified presentation of several differential geometric aspects in the theory of CR manifolds and tangential Cauchy–Riemann equations. It presents the major differential geometric acheivements in the theory of CR manifolds, such as the Tanaka–Webster connection, Fefferman's metric, pseudo-Einstein structures and the Lee conjecture, CR immersions, subelliptic harmonic maps as a local manifestation of pseudoharmonic maps from a CR manifold, Yang–Mills fields on CR manifolds, to name a few. It also aims at explaining how certain results from analysis are employed in CR geometry. Motivated by clear exposition, many examples, explicitly worked-out geometric results, and stimulating unproved statements and comments referring to the most recent aspects of the theory, this monograph is suitable for researchers and graduate students in differential geometry, complex analysis, and PDEs. |
30. Time (Manifold 1) by Stephen Baxter | |
Paperback: 464
Pages
(2000-08-07)
list price: US$14.45 -- used & new: US$21.58 (price subject to change: see help) Asin: 0006511821 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Excellent read |
31. Differential Manifolds (Dover Book on Mathematics) by Antoni A. Kosinski | |
Paperback: 288
Pages
(2007-10-19)
list price: US$15.95 -- used & new: US$4.57 (price subject to change: see help) Asin: 0486462447 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
Captain Obvious Handles Another Review
Almost everything about higher-dim smooth manfolds in 220 pgs
Rigorous but not inaccessible. |
32. Foundations of Hyperbolic Manifolds (Graduate Texts in Mathematics) by John Ratcliffe | |
Paperback: 783
Pages
(2010-11-02)
list price: US$74.95 -- used & new: US$60.14 (price subject to change: see help) Asin: 1441922024 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This heavily class-tested book is an exposition of the theoretical foundations of hyperbolic manifolds. It is a both a textbook and a reference. A basic knowledge of algebra and topology at the first year graduate level of an American university is assumed. The first part is concerned with hyperbolic geometry and discrete groups. The second part is devoted to the theory of hyperbolic manifolds. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. Each chapter contains exercises and a section of historical remarks. A solutions manual is available separately. Customer Reviews (3)
Great reference
Best on the market
An excellent overview for mathematicians and physicists |
33. 3-Manifolds (AMS Chelsea Publishing) by John Hempel | |
Hardcover: 195
Pages
(2004-11)
list price: US$30.00 -- used & new: US$19.97 (price subject to change: see help) Asin: 0821836951 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description The theme of this book is the role of the fundamental group in determining the topology of a given 3-manifold. The essential ideas and techniques are covered in the first part of the book: Heegaard splittings, connected sums, the loop and sphere theorems, incompressible surfaces, free groups, and so on. Along the way, many useful and insightful results are proved, usually in full detail. Later chapters address more advanced topics, including Waldhausen's theorem on a class of 3-manifolds that is completely determined by its fundamental group. The book concludes with a list of problems that were unsolved at the time of publication. Hempel's book remains an ideal text to learn about the world of 3-manifolds. The prerequisites are few and are typical of a beginning graduate student. Exercises occur throughout the text. Other key books on low-dimensional topology available from the AMS are Knots and Links, Lectures on Three-Manifold Topology, and The Knot Book. Customer Reviews (1)
An indispensable classic What this book isn't: What this book is: Some final remarks: |
34. Invariant Manifolds for Physical and Chemical Kinetics (Lecture Notes in Physics) by Alexander N. Gorban, Iliya V. Karlin | |
Paperback: 495
Pages
(2010-11-30)
list price: US$179.00 -- used & new: US$179.00 (price subject to change: see help) Asin: 3642061532 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description By bringing together various ideas and methods for extracting the slow manifolds, the authors show that it is possible to establish a more macroscopic description in nonequilibrium systems. The book treats slowness as stability. A unifying geometrical viewpoint of the thermodynamics of slow and fast motion enables the development of reduction techniques, both analytical and numerical. Examples considered in the book range from the Boltzmann kinetic equation and hydrodynamics to the Fokker-Planck equations of polymer dynamics and models of chemical kinetics describing oxidation reactions. Special chapters are devoted to model reduction in classical statistical dynamics, natural selection, and exact solutions for slow hydrodynamic manifolds. The book will be a major reference source for both theoretical and applied model reduction. Intended primarily as a postgraduate-level text in nonequilibrium kinetics and model reduction, it will also be valuable to PhD students and researchers in applied mathematics, physics and various fields of engineering. |
35. Optimization Algorithms on Matrix Manifolds by P.-A. Absil, R. Mahony, R. Sepulchre | |
Hardcover: 240
Pages
(2007-12-03)
list price: US$52.50 -- used & new: US$32.99 (price subject to change: see help) Asin: 0691132984 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Well done Pierre & Co |
36. Relativity on Curved Manifolds (Cambridge Monographs on Mathematical Physics) by F. de Felice, C. J. S. Clarke | |
Paperback: 464
Pages
(1992-03-27)
list price: US$80.00 -- used & new: US$57.99 (price subject to change: see help) Asin: 0521429080 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
37. Geometric Mechanics on Riemannian Manifolds: Applications to Partial Differential Equations (Applied and Numerical Harmonic Analysis) by Ovidiu Calin, Der-Chen Chang | |
Hardcover: 278
Pages
(2004-10-25)
list price: US$109.00 -- used & new: US$12.96 (price subject to change: see help) Asin: 0817643540 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Differential geometry techniques have very useful and important applications in partial differential equations and quantum mechanics. This work presents a purely geometric treatment of problems in physics involving quantum harmonic oscillators, quartic oscillators, minimal surfaces, Schrödinger's, Einstein's and Newton's equations, and others. Historically, problems in these areas were approached using the Fourier transform or path integrals, although in some cases, e.g., the case of quartic oscillators, these methods do not work. New geometric methods, which have the advantage of providing quantitative or at least qualitative descriptions of operators, many of which cannot be treated by other methods, are introduced. And, conservation laws of the Euler--Lagrange equations are employed to solve the equations of motion qualitatively when quantitative analysis is not possible. Main topics include: Lagrangian formalism on Riemannian manifolds; energy momentum tensor and conservation laws; Hamiltonian formalism; Hamilton--Jacobi theory; harmonic functions, maps, and geodesics; fundamental solutions for heat operators with potential; and variational approach to mechanical curves. The text is enriched with good examples and exercises at the end of every chapter. |
38. Differential and Riemannian Manifolds (Graduate Texts in Mathematics) by Serge Lang | |
Hardcover: 384
Pages
(1995-03-09)
list price: US$79.95 -- used & new: US$41.49 (price subject to change: see help) Asin: 0387943382 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
Modern, but....
Not a "first book", ok as reference
Maybe Lang's best book. So, what's interesting about D&RM? It's a book very much like Lang's other books, only that here the Bourbakist's approach is quite happy: it's one of the very few books on his subject to present most of his results in infinite-dimensional(Banach) version, a must if you are interested in nonlinear functional analysis or dynamical systems. The exposition is very clean and clear: Lang uses categories all the way to estabilish the main relations between the different differential-topological structures and tools, and he does not hesitate in stating and using tools from analysis, such as Lebesgue measure and functional analysis' main theorems. The proofs are very polished and, in a certain sense, beautiful, a philosophy thatpermeates most of the book. As if it weren't enough, the book still contains an appendix with a Von Neumann's seminar about the spectral theorem. All things considered, it's a quite "state-of-the-art" book about the basics of differential manifolds, from an analyst's perspective. This perspective provides differential topology with a lot of additional clarity and power. I don't know if most physicists would like this book, because its motivations, if any, are sparse and sometimes quite obscure, as long as physical applications are concerned. For a mathematician, however, this book is a gem: it's Lang at its best, and the perfect opening door to global analysis (the nonlinear analysis on infinite dimensional manifolds, a vast field of mathematics that encompasses dynamical systems and nonlinear functional analysis). Despite all that, I would also recommend to physicists to at least tackle this book, as an antidote to all the crap that the so-called "differential topology for physicists" books put on their heads, because I don't know a cleaner and more precise presentation of differential manifolds so far. ... Read more |
39. The Arithmetic of Hyperbolic 3-Manifolds (Graduate Texts in Mathematics) by Colin Maclachlan, Alan W. Reid | |
Paperback: 463
Pages
(2010-11-02)
list price: US$79.95 -- used & new: US$64.09 (price subject to change: see help) Asin: 1441931228 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Sweet book on a really interesting topic |
40. The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44) by John W. Morgan | |
Paperback: 130
Pages
(1995-12-11)
list price: US$45.00 -- used & new: US$44.97 (price subject to change: see help) Asin: 0691025975 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces. Customer Reviews (2)
the first book on Seiberg-Witten gauge theory, but not for beginners
Fairly good book on the subject |
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