UID:
almahu_9949697568102882
Format:
1 online resource (265 p.)
ISBN:
1-281-76654-2
,
9786611766542
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0-08-087458-4
Series Statement:
Pure and applied mathematics ; v. 138
Content:
Differential Manifolds is a modern graduate-level introduction to the important field of differential topology. The concepts of differential topology lie at the heart of many mathematical disciplines such as differential geometry and the theory of lie groups. The book introduces both the h-cobordism theorem and the classification of differential structures on spheres. The presentation of a number of topics in a clear and simple fashion make this book an outstanding choice for a graduate course in differential topology as well as for individual study.Key Features* Presents the study
Note:
Description based upon print version of record.
,
Front Cover; Differential Manifolds; Copyright Page; Contents; Introduction; Notational Conventions; Chapter I. Differentiable Structures; 1. Smooth Manifolds and Maps; 2. Partitions of Unity; 3. Smooth Vector Bundles; 4. Tangent Space; 5. Vector Fields; 6. Differential Equations on a Smooth Manifold; 7. Collars; Chapter II. Immersions, Imbeddings, Submanifolds; 1. Local Equivalence of Maps; 2. Submanifolds; 3. Imbeddings in Rn; 4. Isotopies; 5. Ambient Isotopies; 6. Historical Remarks; Chapter III. Normal Bundle, Tubular Neighborhoods; 1. Exponential Map
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2. Normal Bundle and Tubular Neighborhoods3. Uniqueness of Tubular Neighborhoods; 4. Submanifolds of the Boundary; 5. Inverse Image of a Regular Value; 6. The group Gm; 7. Remarks; Chapter IV. Transversality; 1. Transversal Maps and Manifolds; 2. Transversality Theorem; 3. Morse Functions; 4. Neighborhood of a Critical Point; 5. Intersection Numbers; 6. Historical Remarks; Chapter V. Foliations; 1. d-Fields; 2. Foliations; 3. Frobenius Theorem; 4. Leaves of a Foliation; 5. Examples; Chapter VI. Operations on Manifolds; 1. Connected Sum; 2. # and Homotopy Spheres; 3. Boundary Connected Sum
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4. Joining Manifolds along Submanifolds5. Joining Manifolds along Submanifolds of the Boundary; 6. Attaching Handles; 7. Cancellation Lemma; 8. Combinatorial Attachment; 9. Surgery; 10. Homology and Intersections in a Handle; 11. (m, k)-Handlebodies, m 〉 2k; 12. (2k, k)-Handlebodies; Plumbing; Chapter VII. Handle Presentation Theorem; 1. Elementary Cobordisms; 2. Handle Presentation Theorem; 3. Homology Data of a Cobordism; 4. Morse Inequalities; 5. Poincark Duality; 6. 0-Dimensional Handles; 7. Heegaard Diagrams; 8. Historical Remarks; Chapter VIII. The h-Cobordism Theorem
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1. Elementary Row Operations2. Cancellation of Handles; 3. 1-Handles; 4. Minimal Presentation; Main Theorems; 5. h-cobordism; The Group ?m; 6. Highly Connected Manifolds; 7. Remarks; Chapter IX. Framed Manifolds; 1. Framings; 2. Framed Submanifolds; 3. Ok(Mm); 4. Oo(Mm); 5. The Pontriagin Construction; 6. Operations on Framed Submanifolds and Homotopy Theory; 7. p-Manifolds; 8. Almost Parallelizable Manifolds; 9. Historical Remarks; Chapter X. Surgery; 1. Effect of Surgery on Homology; 2. Framing a Surgery; Surgery below Middle Dimension; 3. Surgery on 4n-Dimensional Manifolds
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4. Surgery on (4n + 2)-Dimensional Manifolds5. Surgery on Odd-Dimensional Manifolds; 6. Computation of ?n; 7. Historical Note; Appendix; 1. Implicit Function Theorem; 2. A Lemma of M. Morse; 3. Brown-Sard Theorem; 4. Orthonormalization; 5. Homotopy Groups of SO(k); Bibliography; Index
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English
Additional Edition:
ISBN 0-12-421850-4
Language:
English
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