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The Resource Topological Library  Part 3 : Spectral Sequences in Topology, (electronic resource)
Topological Library  Part 3 : Spectral Sequences in Topology, (electronic resource)
Resource Information
The item Topological Library  Part 3 : Spectral Sequences in Topology, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.This item is available to borrow from all library branches.
Resource Information
The item Topological Library  Part 3 : Spectral Sequences in Topology, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.
This item is available to borrow from all library branches.
 Summary
 The final volume of the threevolume edition, this book features classical papers on algebraic and differential topology published in the 1950s1960s. The partition of these papers among the volumes is rather conditional. 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: Singular homology of fiber spaces  Introduction (
 Language

 eng
 rus
 eng
 Extent
 1 online resource (592 p.)
 Note
 Description based upon print version of record
 Contents

 TOPOLOGICAL LIBRARY; Contents; Foreword; 1. J.P. Serre. Singular homology of fiber spaces (Translated by V. P. Golubyatnikov); Introduction; Chapter I. The notion of spectral sequence; 1. Spectral sequence of a differential group with increasing filtration; 2. The case of graded group; 3. Transgression and suspension; 4. Exact sequence; 5. The cohomology spectral sequence; 6. Spectral sequence of universal covering; Chapter II. Singular homology and cohomology of fiber spaces; 1. Singular cubic homology; 2. Fiber spaces. Definitions and simple properties
 3. Local family composed by homology of fiber4. Filtration of singular complex of the space E; 5. Calculation of the term E1; 6. Calculation of the term E2; 7. Properties of the homology spectral sequences; 8. Cohomology spectral sequence; 9. Properties of the cohomology spectral sequence; 10. Transformation of second terms of homology and cohomology spectral sequences; 11. Proof of Lemma 4; 12. Proof of Lemma 5; 13. Proof of Lemma 3; Chapter III. Applications of spectral sequences of fiber spaces; 1. First application; 2. EulerPoincare characteristic of fiber spaces
 3. Fibrations of Euclidean spaces4. Exact sequence; 5. Gysin exact sequence; 6. Wang exact sequence; 7. LerayHirsch theorem; Chapter IV. Loop spaces; 1. Loop spaces; 2. Hopf theorem; 3. Simplicity of Hspaces; 4. The loop spaces fibrations; 5. Fibration of a path space with fixed origin; 6. Some general results on homology of loop spaces; 7. Applications to variations calculus (Morse theory); 8. Applications to variations calculus: geodesics transversal to two submanifolds; 9. The homology and cohomology of loop space on a sphere; Chapter V. Homotopy groups; 1. General method
 2. First results3. Finiteness of homotopy groups of odddimensional spheres; 4. Auxiliary calculations; 5. The first nontrivial modulo p homotopy group of an odddimensional sphere; 6. Stiefel manifolds and evendimensional spheres; Chapter VI. Groups of EilenbergMacLane; 1. Introduction; 2. General results; 3. The Hopf theorem; Appendix. On homology of some coverings; References; 2. J.P. Serre. Homotopy groups and classes of abelian groups (Translated by V. P. Golubyatnikov); Introduction; Chapter I. The notion of a class; Notations; 1. Definition of classes; 2. enotions
 3. Torsion product4. Two axioms on classes; 5. A new axiom; 6. Examples of classes satisfying axioms (IIA) and (III); 7. Examples of classes satisfying the axioms (lIB) and (III); Chapter II. Fiber spaces; 1. Relative fiber spaces; 2. The homology spectral sequence of a relative fiber space; 3. The cohomology spectral sequence of a relative fibration; 4. The main theorems; 5. Applications; 6. The loop spaces and the EilenbergMacLane groups; Chapter III. The theorems of Hurewicz and J. H. C. Whitehead; 1. Hurewicz theorem; 2. Hurewicz theorem: the second proof; 3. Relative Hurewicz theorem
 4. Theorem of J. H. C. Whitehead
 Isbn
 9789814401319
 Label
 Topological Library  Part 3 : Spectral Sequences in Topology
 Title
 Topological Library  Part 3
 Title remainder
 Spectral Sequences in Topology
 Title variation

 Series on Knots and Everything
 Topological library [ pt. 3
 Topological library
 Topological Library, Part 3
 Series On Knots And Everything vol. 50
 Topological Library  Part 3
 Language

 eng
 rus
 eng
 Summary
 The final volume of the threevolume edition, this book features classical papers on algebraic and differential topology published in the 1950s1960s. The partition of these papers among the volumes is rather conditional. 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: Singular homology of fiber spaces  Introduction (
 Cataloging source
 AUPeEL
 http://library.link/vocab/creatorName
 Novikov, S. P
 Dewey number

 514
 514.2
 LC call number
 QA613.66 .T673 2012
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName

 Taimanov, I. A
 Golubyatnikov, V. P
 Series statement
 Series on Knots and Everything
 http://library.link/vocab/subjectName

 Characteristic classes
 Cobordism theory
 Differential topology
 Label
 Topological Library  Part 3 : Spectral Sequences in Topology, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Contents

 TOPOLOGICAL LIBRARY; Contents; Foreword; 1. J.P. Serre. Singular homology of fiber spaces (Translated by V. P. Golubyatnikov); Introduction; Chapter I. The notion of spectral sequence; 1. Spectral sequence of a differential group with increasing filtration; 2. The case of graded group; 3. Transgression and suspension; 4. Exact sequence; 5. The cohomology spectral sequence; 6. Spectral sequence of universal covering; Chapter II. Singular homology and cohomology of fiber spaces; 1. Singular cubic homology; 2. Fiber spaces. Definitions and simple properties
 3. Local family composed by homology of fiber4. Filtration of singular complex of the space E; 5. Calculation of the term E1; 6. Calculation of the term E2; 7. Properties of the homology spectral sequences; 8. Cohomology spectral sequence; 9. Properties of the cohomology spectral sequence; 10. Transformation of second terms of homology and cohomology spectral sequences; 11. Proof of Lemma 4; 12. Proof of Lemma 5; 13. Proof of Lemma 3; Chapter III. Applications of spectral sequences of fiber spaces; 1. First application; 2. EulerPoincare characteristic of fiber spaces
 3. Fibrations of Euclidean spaces4. Exact sequence; 5. Gysin exact sequence; 6. Wang exact sequence; 7. LerayHirsch theorem; Chapter IV. Loop spaces; 1. Loop spaces; 2. Hopf theorem; 3. Simplicity of Hspaces; 4. The loop spaces fibrations; 5. Fibration of a path space with fixed origin; 6. Some general results on homology of loop spaces; 7. Applications to variations calculus (Morse theory); 8. Applications to variations calculus: geodesics transversal to two submanifolds; 9. The homology and cohomology of loop space on a sphere; Chapter V. Homotopy groups; 1. General method
 2. First results3. Finiteness of homotopy groups of odddimensional spheres; 4. Auxiliary calculations; 5. The first nontrivial modulo p homotopy group of an odddimensional sphere; 6. Stiefel manifolds and evendimensional spheres; Chapter VI. Groups of EilenbergMacLane; 1. Introduction; 2. General results; 3. The Hopf theorem; Appendix. On homology of some coverings; References; 2. J.P. Serre. Homotopy groups and classes of abelian groups (Translated by V. P. Golubyatnikov); Introduction; Chapter I. The notion of a class; Notations; 1. Definition of classes; 2. enotions
 3. Torsion product4. Two axioms on classes; 5. A new axiom; 6. Examples of classes satisfying axioms (IIA) and (III); 7. Examples of classes satisfying the axioms (lIB) and (III); Chapter II. Fiber spaces; 1. Relative fiber spaces; 2. The homology spectral sequence of a relative fiber space; 3. The cohomology spectral sequence of a relative fibration; 4. The main theorems; 5. Applications; 6. The loop spaces and the EilenbergMacLane groups; Chapter III. The theorems of Hurewicz and J. H. C. Whitehead; 1. Hurewicz theorem; 2. Hurewicz theorem: the second proof; 3. Relative Hurewicz theorem
 4. Theorem of J. H. C. Whitehead
 Dimensions
 unknown
 Extent
 1 online resource (592 p.)
 Form of item
 electronic
 Isbn
 9789814401319
 Specific material designation
 remote
 System control number

 (CKB)3280000000006439
 (EBL)1679569
 (WSP)00002927
 (EXLCZ)993280000000006439
 Label
 Topological Library  Part 3 : Spectral Sequences in Topology, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Contents

 TOPOLOGICAL LIBRARY; Contents; Foreword; 1. J.P. Serre. Singular homology of fiber spaces (Translated by V. P. Golubyatnikov); Introduction; Chapter I. The notion of spectral sequence; 1. Spectral sequence of a differential group with increasing filtration; 2. The case of graded group; 3. Transgression and suspension; 4. Exact sequence; 5. The cohomology spectral sequence; 6. Spectral sequence of universal covering; Chapter II. Singular homology and cohomology of fiber spaces; 1. Singular cubic homology; 2. Fiber spaces. Definitions and simple properties
 3. Local family composed by homology of fiber4. Filtration of singular complex of the space E; 5. Calculation of the term E1; 6. Calculation of the term E2; 7. Properties of the homology spectral sequences; 8. Cohomology spectral sequence; 9. Properties of the cohomology spectral sequence; 10. Transformation of second terms of homology and cohomology spectral sequences; 11. Proof of Lemma 4; 12. Proof of Lemma 5; 13. Proof of Lemma 3; Chapter III. Applications of spectral sequences of fiber spaces; 1. First application; 2. EulerPoincare characteristic of fiber spaces
 3. Fibrations of Euclidean spaces4. Exact sequence; 5. Gysin exact sequence; 6. Wang exact sequence; 7. LerayHirsch theorem; Chapter IV. Loop spaces; 1. Loop spaces; 2. Hopf theorem; 3. Simplicity of Hspaces; 4. The loop spaces fibrations; 5. Fibration of a path space with fixed origin; 6. Some general results on homology of loop spaces; 7. Applications to variations calculus (Morse theory); 8. Applications to variations calculus: geodesics transversal to two submanifolds; 9. The homology and cohomology of loop space on a sphere; Chapter V. Homotopy groups; 1. General method
 2. First results3. Finiteness of homotopy groups of odddimensional spheres; 4. Auxiliary calculations; 5. The first nontrivial modulo p homotopy group of an odddimensional sphere; 6. Stiefel manifolds and evendimensional spheres; Chapter VI. Groups of EilenbergMacLane; 1. Introduction; 2. General results; 3. The Hopf theorem; Appendix. On homology of some coverings; References; 2. J.P. Serre. Homotopy groups and classes of abelian groups (Translated by V. P. Golubyatnikov); Introduction; Chapter I. The notion of a class; Notations; 1. Definition of classes; 2. enotions
 3. Torsion product4. Two axioms on classes; 5. A new axiom; 6. Examples of classes satisfying axioms (IIA) and (III); 7. Examples of classes satisfying the axioms (lIB) and (III); Chapter II. Fiber spaces; 1. Relative fiber spaces; 2. The homology spectral sequence of a relative fiber space; 3. The cohomology spectral sequence of a relative fibration; 4. The main theorems; 5. Applications; 6. The loop spaces and the EilenbergMacLane groups; Chapter III. The theorems of Hurewicz and J. H. C. Whitehead; 1. Hurewicz theorem; 2. Hurewicz theorem: the second proof; 3. Relative Hurewicz theorem
 4. Theorem of J. H. C. Whitehead
 Dimensions
 unknown
 Extent
 1 online resource (592 p.)
 Form of item
 electronic
 Isbn
 9789814401319
 Specific material designation
 remote
 System control number

 (CKB)3280000000006439
 (EBL)1679569
 (WSP)00002927
 (EXLCZ)993280000000006439
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