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41. Branched Standard Spines of 3-manifolds (Lecture Notes in Mathematics) by Riccardo Benedetti, Carlo Petronio | |
Paperback: 132
Pages
(1997-04-18)
list price: US$30.00 -- used & new: US$23.50 (price subject to change: see help) Asin: 3540626271 Canada | United Kingdom | Germany | France | Japan | |
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42. 4-Manifolds and Kirby Calculus (Graduate Studies in Mathematics) by Andras I. Stipsicz Robert E. Gompf | |
Hardcover: 558
Pages
(1999-08-31)
list price: US$71.00 -- used & new: US$71.00 (price subject to change: see help) Asin: 0821809946 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
Review
Extremely detailed overview of Kirby calculus Kirby calculus can be used to describe four-dimensional manifolds such as elliptic surfaces, and gives a pictorial description of its handle decomposition. Its utility lies further than this however, as Kirby calculus has been used to answer questions that would have been very difficult otherwise. The book begins with a very quick overview of the algebraic topology and gauge theory of four-dimensional manifolds. Readers not familiar with this material will have to consult other books or papers on the subject. Part two takes up Kirby calculus, and handle decompositions are described with examples given for disk bundles over surfaces and tori. Handle moves are employed as processes that allow one to go from one description of a manifold to another. Handlebody descriptions are given for spin manifolds, and more exotic topics, such as Casson handles and branched covers are treated. Part 3 of the book uses techniques from algebraic geometry to describe branched covers of algebraic surfaces. Handle decompositions of Lefschetz fibrations are given, and its is shown that a Stein structure on a manifold is completely described by a handle diagram. There is also a thorough discussion of exotic structures on Euclidean 4-space. In spite of the non-constructive nature of these results, namely that no explicit example of an exotic structure is given, the discussion is a fascinating one and has recently been shown to be important in physics. The reader will no doubt attempt many of the exercises; the solutions of some of these given in the back of the book. The book serves well the needs of those dedicated individuals who are interested in specializing in low-dimensional topology. In addition, physicists interested in these ideas couuld benefit from its reading, although some of the results may seem a little heavy-handed and abtruse at times.
Complexity is the name... |
43. An Introduction to Differential Manifolds by Dennis Barden, Charles B. Thomas | |
Paperback: 232
Pages
(2003-03)
list price: US$37.00 -- used & new: US$29.89 (price subject to change: see help) Asin: 1860943551 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
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A mile wide and a yard deep
This book Rules! |
44. The Equilibrium Manifold: Postmodern Developments in the Theory of General Economic Equilibrium (Arne Ryde Memorial Lecture Series) by Yves Balasko | |
Hardcover: 264
Pages
(2009-05-29)
list price: US$37.00 -- used & new: US$21.84 (price subject to change: see help) Asin: 0262026546 Canada | United Kingdom | Germany | France | Japan | |
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45. CR Manifolds and the Tangential Cauchy Riemann Complex (Studies in Advanced Mathematics) by Albert Boggess | |
Hardcover: 384
Pages
(1991-09-12)
list price: US$173.95 -- used & new: US$148.76 (price subject to change: see help) Asin: 084937152X Canada | United Kingdom | Germany | France | Japan | |
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46. Classical Tesselations and Three-Manifolds (Universitext) by Jose M. Montesinos-Amilibia | |
Paperback: 230
Pages
(1987-09-01)
list price: US$61.95 -- used & new: US$39.99 (price subject to change: see help) Asin: 3540152911 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Solves the Alhambra mystery! The book includes pictures of all the 17 wallpaper groups from Alhambra. It should however be pointed out that in his review of the paper by Perez-Gomez in Mathematical Reviews, Coxeter disputes the p3m1 example. ... Read more |
47. Theory of Engine Manifold Design: Wave Action Methods for IC Engines by Desmond E. Winterbone, Richard J. Pearson | |
Hardcover: 512
Pages
(2005-07-18)
list price: US$215.00 -- used & new: US$237.00 (price subject to change: see help) Asin: 1860582095 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description CONTENTS INCLUDE: |
48. Seiberg-Witten and Gromov invariants for symplectic 4-manifolds (2010 re-issue) by Clifford Henry Taubes | |
Paperback: 412
Pages
(2010-06-02)
list price: US$35.00 -- used & new: US$35.00 (price subject to change: see help) Asin: 1571462031 Canada | United Kingdom | Germany | France | Japan | |
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49. 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 |
50. Manifold Theory: An Introduction for Mathematical Physicists by Daniel Martin | |
Paperback: 424
Pages
(2002-08)
list price: US$85.00 -- used & new: US$57.95 (price subject to change: see help) Asin: 1898563845 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
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required reading |
51. Geometry of Low-Dimensional Manifolds, Vol. 1: Gauge Theory and Algebraic Surfaces (London Mathematical Society Lecture Note Series) | |
Paperback: 276
Pages
(1991-01-25)
list price: US$60.00 -- used & new: US$46.42 (price subject to change: see help) Asin: 0521399785 Canada | United Kingdom | Germany | France | Japan | |
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52. Geometry of Low-Dimensional Manifolds, Vol. 2: Symplectic Manifolds and Jones-Witten Theory (London Mathematical Society Lecture Note Series) | |
Paperback: 260
Pages
(1991-01-25)
list price: US$70.00 -- used & new: US$12.50 (price subject to change: see help) Asin: 0521400015 Canada | United Kingdom | Germany | France | Japan | |
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53. Infinite Dimensional Kähler Manifolds (Oberwolfach Seminars) | |
Paperback: 375
Pages
(2001-09-21)
list price: US$59.95 -- used & new: US$40.08 (price subject to change: see help) Asin: 3764366028 Canada | United Kingdom | Germany | France | Japan | |
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54. Introduction to Differentiable Manifolds by Louis Auslander, Robert E. MacKenzie | |
Paperback: 224
Pages
(2009-02-19)
list price: US$12.95 -- used & new: US$5.95 (price subject to change: see help) Asin: 0486471721 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Saved me in grad school
out-of-date; even worse, sometimes incorrect |
55. Hyperbolic manifolds and holomorphic mappings (Pure and applied mathematics, 2) by Shoshichi Kobayashi | |
Hardcover: 148
Pages
(1970)
Isbn: 082471380X Canada | United Kingdom | Germany | France | Japan | |
56. Einstein Manifolds (Classics in Mathematics) by Arthur L. Besse | |
Paperback: 516
Pages
(2007-12-18)
list price: US$69.95 -- used & new: US$48.82 (price subject to change: see help) Asin: 3540741208 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Einstein's equations stem from General Relativity. In the context of Riemannian manifolds, an independent mathematical theory has developed around them. Recently, it has produced several striking results, which have been of great interest also to physicists. This Ergebnisse volume is the first book which presents an up-to-date overview of the state of the art in this field. "Einstein Manifold"s is a successful attempt to organize the abundant literature, with emphasis on examples. Parts of it can be used separately as introduction to modern Riemannian geometry through topics like homogeneous spaces, submersions, or Riemannian functionals. |
57. Involutions on Manifolds (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete) by Santiago Lopez De Medrano | |
Hardcover: 102
Pages
(1971-05)
list price: US$59.95 Isbn: 0387050922 Canada | United Kingdom | Germany | France | Japan | |
58. Manifolds All of Whose Geodesics Are Closed (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge) (English and French Edition) by A. L. Besse | |
Hardcover: 262
Pages
(1978-06-07)
list price: US$189.00 -- used & new: US$138.35 (price subject to change: see help) Asin: 3540081585 Canada | United Kingdom | Germany | France | Japan | |
59. Compact Manifolds with Special Holonomy (Oxford Mathematical Monographs) by Dominic D. Joyce | |
Hardcover: 448
Pages
(2000-09-21)
list price: US$170.00 -- used & new: US$100.00 (price subject to change: see help) Asin: 0198506015 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
WELL DONE! |
60. Differential Geometry: Curves - Surfaces - Manifolds, Second Edition by Wolfgang Kühnel | |
Paperback: 380
Pages
(2005-12-13)
list price: US$51.00 -- used & new: US$40.80 (price subject to change: see help) Asin: 0821839888 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (5)
elegant work
Fast moving
A excellent introduction for the 21st century
A beautiful geometry
Attractive book on differential geometry |
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