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The Resource Topological Library - Part 2 : Characteristic Classes And Smooth Structures On Manifolds

Topological Library - Part 2 : Characteristic Classes And Smooth Structures On Manifolds

Summary
This is the second of a three-volume set collecting the original and now-classic works in topology written during the 1950s-1960s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated "singular homologies of fiber spaces.". Sample Chapter(s). Chapter 1: On manifolds homeomorphic to the 7-sphere 1 (153 KB). Contents: On Manifolds Homeomorphic to the 7-Sphere (J Milnor); Groups of Homotopy Sphe
Language
eng
Work
Publication
Extent
1 online resource (280)
Contents
  • Cover13;
  • Contents
  • S.P. Novikovs Preface
  • 1 J. Milnor. On manifolds homeomorphic to the 7-sphere
  • 167; 1. The invariant 955;(M7)
  • 167; 2. A partial characterization of the n-sphere
  • 167; 3. Examples of 7-manifolds
  • 167; 4. Miscellaneous results
  • References
  • 2 M. Kervaire and J. Milnor. Groups of homotopy spheres. I
  • 167;1. Introduction
  • 167; 2. Construction of the group 920;n
  • 167; 3. Homotopy spheres are s-parallelizable
  • 167; 4. Which homotopy spheres bound parallelizable manifolds?
  • 167; 5. Spherical modifications
  • 167; 6. Framed sphericalmodifications
  • 167; 7. The groups bP2k
  • 167; 8. A cohomology operation
  • References
  • 3 S.P. Novikov. Homotopically equivalent smooth manifolds
  • Introduction
  • Chapter I. The fundamental construction
  • 167; 1. Morses surgery
  • 167; 2. Relative 960;-manifolds
  • 167; 3. The general construction
  • 167; 4. Realization of classes
  • 167; 5. The manifolds in one class
  • 167; 6. Onemanifold in different classes
  • Chapter II. Processing the results
  • 167; 7. The Thom space of a normal bundle. Its homotopy structure
  • 167; 8. Obstructions to a di.eomorphism of manifolds having the same homotopy type and a stable normal bundle
  • 167; 9. Variation of a smooth structure keeping triangulation preserved
  • 167; 10. Varying smooth structure and keeping the triangulation preserved. Morse surgery
  • Chapter III. Corollaries and applications
  • 167; 11. Smooth structures on Cartesian product of spheres
  • 167; 12. Low-dimensional manifolds. Cases n = 4, 5, 6, 7
  • 167; 13. Connected sum of a manifold with Milnors sphere
  • 167; 14. Normal bundles of smooth manifolds
  • Appendix 1. Homotopy type and Pontrjagin classes
  • Appendix 2. Combinatorial equivalence and Milnors microbundle theory
  • Appendix 3. On groups
  • Appendix 4. Embedding of homotopy spheres into Euclidean space and the suspension stable homomorphism
  • References
  • 4 S.P. Novikov. Rational Pontrjagin classes. Homeomorphism and homotopy type of closed manifolds
  • Introduction
  • 167; 1. Signature of a cycle and its properties
  • 167; 2. The basic lemma
  • 167; 3. Theorems on homotopy invariance. Generalized signature theorem
  • 167; 4. The topological invariance theorem
  • 167; 5. Consequences of the topological invariance theorem
  • Appendix (V.A. Rokhlin). Diffeomorphisms of the manifold S2 215; S3
  • References
  • 5 S.P. Novikov. On manifolds with free abelian fundamental group and their applications (Pontrjagin classes, smooth structures, high-dimensional knots)
  • Introduction
  • 167; 1. Formulation of results
  • 167; 2. The proof scheme of main theorems
  • 167; 3. A geometrical lemma
  • 167; 4. An analog of the Hurewicz theorem
  • 167; 5. The functor P = Homc and its application to the study of homology properties of degree one maps
  • 167; 6. Stably freeness of kernel modules under the assumptions of Theorem 3
  • 167; 7. The homology effect of a Morse surgery
  • 167; 8. Proof of Theorem 3
  • 167; 9. Proof of Theorem 6
  • 167; 10. One generalization of Theorem 5
  • Appendix 1. On the signature formula
  • Appendix 2. Unsolved questions concerning characteristic class theory
  • Appendix 3. Algebraic remarks about the functor P = Homc
  • References
  • 6 R. Kirby. Stable homeomorphisms and the annulus conjecture
Isbn
9789812836878
Instance
Label
Topological Library - Part 2 : Characteristic Classes And Smooth Structures On Manifolds
Title
Topological Library - Part 2
Title remainder
Characteristic Classes And Smooth Structures On Manifolds
Subject
Language
eng
Summary
This is the second of a three-volume set collecting the original and now-classic works in topology written during the 1950s-1960s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated "singular homologies of fiber spaces.". Sample Chapter(s). Chapter 1: On manifolds homeomorphic to the 7-sphere 1 (153 KB). Contents: On Manifolds Homeomorphic to the 7-Sphere (J Milnor); Groups of Homotopy Sphe
Member of
Cataloging source
IDEBK
Dewey number
514.72
Index
no index present
LC call number
QA613.66
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/subjectName
  • Cobordism theory
  • Characteristic classes
  • Differential topology
  • Characteristic classes
  • Cobordism theory
  • Differential topology
Label
Topological Library - Part 2 : Characteristic Classes And Smooth Structures On Manifolds
Instantiates
Publication
Antecedent source
unknown
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Cover13; -- Contents -- S.P. Novikovs Preface -- 1 J. Milnor. On manifolds homeomorphic to the 7-sphere -- 167; 1. The invariant 955;(M7) -- 167; 2. A partial characterization of the n-sphere -- 167; 3. Examples of 7-manifolds -- 167; 4. Miscellaneous results -- References -- 2 M. Kervaire and J. Milnor. Groups of homotopy spheres. I -- 167;1. Introduction -- 167; 2. Construction of the group 920;n -- 167; 3. Homotopy spheres are s-parallelizable -- 167; 4. Which homotopy spheres bound parallelizable manifolds? -- 167; 5. Spherical modifications -- 167; 6. Framed sphericalmodifications -- 167; 7. The groups bP2k -- 167; 8. A cohomology operation -- References -- 3 S.P. Novikov. Homotopically equivalent smooth manifolds -- Introduction -- Chapter I. The fundamental construction -- 167; 1. Morses surgery -- 167; 2. Relative 960;-manifolds -- 167; 3. The general construction -- 167; 4. Realization of classes -- 167; 5. The manifolds in one class -- 167; 6. Onemanifold in different classes -- Chapter II. Processing the results -- 167; 7. The Thom space of a normal bundle. Its homotopy structure -- 167; 8. Obstructions to a di.eomorphism of manifolds having the same homotopy type and a stable normal bundle -- 167; 9. Variation of a smooth structure keeping triangulation preserved -- 167; 10. Varying smooth structure and keeping the triangulation preserved. Morse surgery -- Chapter III. Corollaries and applications -- 167; 11. Smooth structures on Cartesian product of spheres -- 167; 12. Low-dimensional manifolds. Cases n = 4, 5, 6, 7 -- 167; 13. Connected sum of a manifold with Milnors sphere -- 167; 14. Normal bundles of smooth manifolds -- Appendix 1. Homotopy type and Pontrjagin classes -- Appendix 2. Combinatorial equivalence and Milnors microbundle theory -- Appendix 3. On groups -- Appendix 4. Embedding of homotopy spheres into Euclidean space and the suspension stable homomorphism -- References -- 4 S.P. Novikov. Rational Pontrjagin classes. Homeomorphism and homotopy type of closed manifolds -- Introduction -- 167; 1. Signature of a cycle and its properties -- 167; 2. The basic lemma -- 167; 3. Theorems on homotopy invariance. Generalized signature theorem -- 167; 4. The topological invariance theorem -- 167; 5. Consequences of the topological invariance theorem -- Appendix (V.A. Rokhlin). Diffeomorphisms of the manifold S2 215; S3 -- References -- 5 S.P. Novikov. On manifolds with free abelian fundamental group and their applications (Pontrjagin classes, smooth structures, high-dimensional knots) -- Introduction -- 167; 1. Formulation of results -- 167; 2. The proof scheme of main theorems -- 167; 3. A geometrical lemma -- 167; 4. An analog of the Hurewicz theorem -- 167; 5. The functor P = Homc and its application to the study of homology properties of degree one maps -- 167; 6. Stably freeness of kernel modules under the assumptions of Theorem 3 -- 167; 7. The homology effect of a Morse surgery -- 167; 8. Proof of Theorem 3 -- 167; 9. Proof of Theorem 6 -- 167; 10. One generalization of Theorem 5 -- Appendix 1. On the signature formula -- Appendix 2. Unsolved questions concerning characteristic class theory -- Appendix 3. Algebraic remarks about the functor P = Homc -- References -- 6 R. Kirby. Stable homeomorphisms and the annulus conjecture
Control code
729020484
Dimensions
unknown
Extent
1 online resource (280)
File format
unknown
Form of item
online
Isbn
9789812836878
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
unknown
Reformatting quality
unknown
Specific material designation
remote
System control number
(OCoLC)729020484
Label
Topological Library - Part 2 : Characteristic Classes And Smooth Structures On Manifolds
Publication
Antecedent source
unknown
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Cover13; -- Contents -- S.P. Novikovs Preface -- 1 J. Milnor. On manifolds homeomorphic to the 7-sphere -- 167; 1. The invariant 955;(M7) -- 167; 2. A partial characterization of the n-sphere -- 167; 3. Examples of 7-manifolds -- 167; 4. Miscellaneous results -- References -- 2 M. Kervaire and J. Milnor. Groups of homotopy spheres. I -- 167;1. Introduction -- 167; 2. Construction of the group 920;n -- 167; 3. Homotopy spheres are s-parallelizable -- 167; 4. Which homotopy spheres bound parallelizable manifolds? -- 167; 5. Spherical modifications -- 167; 6. Framed sphericalmodifications -- 167; 7. The groups bP2k -- 167; 8. A cohomology operation -- References -- 3 S.P. Novikov. Homotopically equivalent smooth manifolds -- Introduction -- Chapter I. The fundamental construction -- 167; 1. Morses surgery -- 167; 2. Relative 960;-manifolds -- 167; 3. The general construction -- 167; 4. Realization of classes -- 167; 5. The manifolds in one class -- 167; 6. Onemanifold in different classes -- Chapter II. Processing the results -- 167; 7. The Thom space of a normal bundle. Its homotopy structure -- 167; 8. Obstructions to a di.eomorphism of manifolds having the same homotopy type and a stable normal bundle -- 167; 9. Variation of a smooth structure keeping triangulation preserved -- 167; 10. Varying smooth structure and keeping the triangulation preserved. Morse surgery -- Chapter III. Corollaries and applications -- 167; 11. Smooth structures on Cartesian product of spheres -- 167; 12. Low-dimensional manifolds. Cases n = 4, 5, 6, 7 -- 167; 13. Connected sum of a manifold with Milnors sphere -- 167; 14. Normal bundles of smooth manifolds -- Appendix 1. Homotopy type and Pontrjagin classes -- Appendix 2. Combinatorial equivalence and Milnors microbundle theory -- Appendix 3. On groups -- Appendix 4. Embedding of homotopy spheres into Euclidean space and the suspension stable homomorphism -- References -- 4 S.P. Novikov. Rational Pontrjagin classes. Homeomorphism and homotopy type of closed manifolds -- Introduction -- 167; 1. Signature of a cycle and its properties -- 167; 2. The basic lemma -- 167; 3. Theorems on homotopy invariance. Generalized signature theorem -- 167; 4. The topological invariance theorem -- 167; 5. Consequences of the topological invariance theorem -- Appendix (V.A. Rokhlin). Diffeomorphisms of the manifold S2 215; S3 -- References -- 5 S.P. Novikov. On manifolds with free abelian fundamental group and their applications (Pontrjagin classes, smooth structures, high-dimensional knots) -- Introduction -- 167; 1. Formulation of results -- 167; 2. The proof scheme of main theorems -- 167; 3. A geometrical lemma -- 167; 4. An analog of the Hurewicz theorem -- 167; 5. The functor P = Homc and its application to the study of homology properties of degree one maps -- 167; 6. Stably freeness of kernel modules under the assumptions of Theorem 3 -- 167; 7. The homology effect of a Morse surgery -- 167; 8. Proof of Theorem 3 -- 167; 9. Proof of Theorem 6 -- 167; 10. One generalization of Theorem 5 -- Appendix 1. On the signature formula -- Appendix 2. Unsolved questions concerning characteristic class theory -- Appendix 3. Algebraic remarks about the functor P = Homc -- References -- 6 R. Kirby. Stable homeomorphisms and the annulus conjecture
Control code
729020484
Dimensions
unknown
Extent
1 online resource (280)
File format
unknown
Form of item
online
Isbn
9789812836878
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
unknown
Reformatting quality
unknown
Specific material designation
remote
System control number
(OCoLC)729020484

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