Kooperativer Bibliotheksverbund

UID:

Format: XXVII, 380 S.

ISBN: 3-11-012488-2 , 0-89925-697-X

Series Statement: De Gruyter expositions in mathematics 2

Note: Literaturverz. S. 369 - 372

Language: English

Subjects: Mathematics

Keywords: Komplex ; Dimension 4 ; Homotopie ; Komplex ; Homotopietheorie ; Komplex ; Dimension 4 ; Kombinatorische Homotopie ; Kombinatorische Topologie

URL: Inhaltsverzeichnis

URL: Inhaltstext

Author information: Baues, Hans J. 1943-

UID:

Format: 1 online resource (380 p.)

Edition: Reprint 2011

ISBN: 9783110854480 , 9783110494969

Series Statement: De Gruyter Expositions in Mathematics , 2

Note: Frontmatter -- , Chapter I. Homotopy, homology, and Whitehead's classification of simply connected 4-dimensional CW-complexes -- , Chapter II. The CW-tower of categories -- , Chapter III. Crossed modules and homotopy systems of order 3 -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 1 Quadratic modules -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 2 Free quadratic modules -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 3 Quadratic chain complexes -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 4 Homotopies for quadratic chain maps -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 5 Cofibrations in the category of quadratic chain complexes -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 6 The secondary homotopy addition lemma and a model functor from spaces to quadratic chain complexes -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 7 Homotopy systems of order 4 -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 8 The homotopy category of 3-dimensional CW-complexes -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 9 The CW-tower in degree ≤ 4 -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 10 The homotopy category of 3-types -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 11 The action of the fundamental group for quadratic chain complexes -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 12 The quadratic chain complex of a product -- , Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix A. Some diverse examples and applications of quadratic chain complexes -- , Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix B. Quadratic chain complexes and simplicial groups -- , Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix C. Reduced and stable quadratic modules -- , Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix D. On the homotopy classification of semi free group actions -- , Chapter V. Cohomological invariants -- , Chapter VI. The cohomology of categories and the calculus of tracks -- , Bibliography -- , List of Symbols -- , Index , Issued also in print. , Mode of access: Internet via World Wide Web. , In English.

In: DG Expositions in Mathematics Backlist eBook Package, De Gruyter, 9783110494969

In: DGBA Mathematics - 1990 - 1999, De Gruyter, 9783110637199

In: E-DITION: BEST OF MATHEMATICS, De Gruyter, 9783110233957

Additional Edition: ISBN 9783110124880

Language: English

Subjects: Mathematics

DOI: 10.1515/9783110854480

URL: https://doi.org/10.1515/9783110854480

URL: https://www.degruyter.com/isbn/9783110854480

URL: Cover

UID:

Format: Online-Ressource (xxvii, 380 p) , ill

Edition: Online-Ausg. Palo Alto, Calif ebrary 2011 Electronic reproduction; Available via World Wide Web

ISBN: 089925697X (acid-free) , 3110124882 (acid-free) , 9783110124880 (acid-free)

Series Statement: De Gruyter expositions in mathematics 2

Content: Combinatorial Homotopy and 4-Dimensional Complexes (Architektur Auf Naxos Und Paros)

Note: Includes bibliographical references (p. [369]-372) and index , 1 Linear extensions of categories and exact sequences for functors 2 Homotopy systems of order (n + 1); 3 The CW-tower of categories; 4 The Postnikov chain functor; 5 Three formulas for the obstruction; 6 Trees of homotopy types; 7 On the homotopy classification of manifolds with finite fundamental group; Chapter III. Crossed modules and homotopy systems of order 3; 1 Nilpotent groups and Peiffer nilpotent pre-crossed modules; 2 Crossed chain complexes and homotopy systems of order 3; 3 Cylinders of CW-complexes and of crossed chain complexes. , 11 The action of the fundamental group for quadratic chain complexes 12 The quadratic chain complex of a product; Appendix A. Some diverse examples and applications of quadratic chain complexes; Appendix B. Quadratic chain complexes and simplicial groups; Appendix C. Reduced and stable quadratic modules; Appendix D. On the homotopy classification of semi free group actions; Chapter V. Cohomological invariants; 1 The classification of 4-dimensional homotopy types; 2 A new cohomological invariant and the cup product. , 3 Obstructions for the existence of certain chain maps and the primary obstruction for the realizability of a chain complex. , 4 Cofibrations in the category of crossed chain complexes 5 The homotopy addition lemma; 6 A model functor from spaces to crossed chain complexes; 7 The homotopy category of 2-dimensional CW-complexes; 8 The homotopy category of 2-types; 9 The crossed chain complex of a product; 10 The action of the fundamental group and free homotopy classes; Appendix A. Obstructions for the realizability of chain complexes; Appendix B. The homotopy category of pseudo projective planes; Appendix C. On the suspension and the James construction. , Appendix D. The homotopy category of suspended pseudo projective planesChapter IV. Quadratic modules and homotopy systems of order 4; 1 Quadratic modules; 2 Free quadratic modules; 3 Quadratic chain complexes; 4 Homotopies for quadratic chain maps; 5 Cofibrations in the category of quadratic chain complexes; 6 The secondary homotopy addition lemma and a model functor from spaces to quadratic chain complexes; 7 Homotopy systems of order 4; 8 The homotopy category of 3-dimensional CW-complexes; 9 The CW-tower in degree ≤ 4; 10 The homotopy category of 3-types. , Preface by Ronald Brown; Introduction; Chapter I. Homotopy, homology, and Whitehead's classification of simply connected 4-dimensional CW-complexes; 0 Sufficiency, realizability and detecting functors; 1 Homotopy groups; 2 CW-complexes and homology with local coefficients; 3 Whitehead's certain exact sequence; 4 The quadratic functor Γ and central extensions; 5 Cup products and Pontrjagin squares; 6 Cohomological invariants; 7 An2-polyhedra and An2-forms; 8 Whitehead's classification of An2-polyhedra, n ≥ 2; Chapter II. The CW-tower of categories.

Additional Edition: ISBN 9783110854480

Language: English

DOI: 10.1515/9783110854480

URL: http://www.degruyter.com/doi/book/10.1515/9783110854480

URL: Cover

UID:

Format: 1 online resource (408 p.)

Edition: Reprint 2011

ISBN: 3-11-085448-1

Series Statement: De Gruyter Expositions in Mathematics ; 2

Content: Combinatorial Homotopy and 4-Dimensional Complexes (Architektur Auf Naxos Und Paros)

Note: Description based upon print version of record. , Front matter -- , Chapter I. Homotopy, homology, and Whitehead's classification of simply connected 4-dimensional CW-complexes -- , Chapter II. The CW-tower of categories -- , Chapter III. Crossed modules and homotopy systems of order 3 -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 1 Quadratic modules -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 2 Free quadratic modules -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 3 Quadratic chain complexes -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 4 Homotopies for quadratic chain maps -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 5 Cofibrations in the category of quadratic chain complexes -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 6 The secondary homotopy addition lemma and a model functor from spaces to quadratic chain complexes -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 7 Homotopy systems of order 4 -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 8 The homotopy category of 3-dimensional CW-complexes -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 9 The CW-tower in degree ≤ 4 -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 10 The homotopy category of 3-types -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 11 The action of the fundamental group for quadratic chain complexes -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 12 The quadratic chain complex of a product -- , Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix A. Some diverse examples and applications of quadratic chain complexes -- , Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix B. Quadratic chain complexes and simplicial groups -- , Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix C. Reduced and stable quadratic modules -- , Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix D. On the homotopy classification of semi free group actions -- , Chapter V. Cohomological invariants -- , Chapter VI. The cohomology of categories and the calculus of tracks -- , Bibliography -- , List of Symbols -- , Index , Issued also in print. , English

Additional Edition: ISBN 3-11-012488-2

Language: English

Subjects: Mathematics

DOI: 10.1515/9783110854480

UID:

Format: 1 online resource (407p.)

Edition: Reprint 2011

ISBN: 9783110854480

Series Statement: De Gruyter Expositions in Mathematics ; 2

Note: Frontmatter -- , Chapter I. Homotopy, homology, and Whitehead’s classification of simply connected 4-dimensional CW-complexes -- , Chapter II. The CW-tower of categories -- , Chapter III. Crossed modules and homotopy systems of order 3 -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 1 Quadratic modules -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 2 Free quadratic modules -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 3 Quadratic chain complexes -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 4 Homotopies for quadratic chain maps -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 5 Cofibrations in the category of quadratic chain complexes -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 6 The secondary homotopy addition lemma and a model functor from spaces to quadratic chain complexes -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 7 Homotopy systems of order 4 -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 8 The homotopy category of 3-dimensional CW-complexes -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 9 The CW-tower in degree ≤ 4 -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 10 The homotopy category of 3-types -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 11 The action of the fundamental group for quadratic chain complexes -- , Chapter IV. Quadratic modules and homotopy systems of order 4. § 12 The quadratic chain complex of a product -- , Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix A. Some diverse examples and applications of quadratic chain complexes -- , Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix B. Quadratic chain complexes and simplicial groups -- , Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix C. Reduced and stable quadratic modules -- , Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix D. On the homotopy classification of semi free group actions -- , Chapter V. Cohomological invariants -- , Chapter VI. The cohomology of categories and the calculus of tracks -- , Bibliography -- , List of Symbols -- , Index , In English.

Additional Edition: ISBN 978-3-11-012488-0

Language: English

DOI: 10.1515/9783110854480

URL: https://doi.org/10.1515/9783110854480