James Complexes and Manifolds

The Mathematical Works of J. H. C. Whitehead
1. Auflage 2014
ISBN: 978-1-4831-5029-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 450 Seiten, Web PDF

The Mathematical Works of J. H. C. Whitehead, Volume 2: Complexes and Manifolds contains papers that are related in some way to the classification problem for manifolds, especially the Poincare conjecture, but towards the end one sees the gradual transition in the direction of algebraic topology. This volume includes all Whitehead's published work up to the year 1941, as well as a few later papers. The book begins with a list of Whitehead's works, in chronological order of writing. This is followed by separate chapters on topics such as analytical complexes; duality and intersection chains in combinatorial analysis situs; three-dimensional manifolds; doubled knots; certain sets of elements in a free group; certain invariants introduced by Reidemeister; and the asphericity of regions in a 3-sphere. Also included are chapters on the homotopy type of manifolds; the incidence matrices, nuclei and homotopy types; vector fields on the n-sphere; and operators in relative homotopy groups.

Autoren/Hrsg.

James, I. M.

Inhaltsverzeichnis

1;Front Cover;1
2;Complexes and Manifolds
;4
3;Copyright Page;5
4;Table of Contents;8
5;EDITORIAL PREFACE;6
6;ACKNOWLEDGMENT;7
7;PUBLICATIONS OF J. H. C. WHITEHEAD;10
8;Chapter 1. ON ANALYTICAL COMPLEXES;16
9;Chapter 2. ON DUALITY AND INTERSECTION CHAINS IN COMBINATORIAL ANALYSIS SITUS;24
10;Chapter 3. ON SUBDIVISIONS OF COMPLEXES;28
11;Chapter 4. CERTAIN THEOREMS ABOUT THREE DIMENSIONAL MANIFOLDS (I);36
12;Chapter 5. THREE-DIMENSIONAL MANIFOLDS (CORRIGENDUM);50
13;Chapter 6. A CERTAIN REGION IN EUCLIDEAN 3-SPACE;52
14;Chapter 7. A CERTAIN OPEN MANIFOLD WHOSE GROUP IS UNITY;54
15;Chapter 8. ON THE GROUP OF A CERTAIN LINKAGE;66
16;Chapter 9. ON DOUBLED KNOTS;74
17;Chapter 10. ON CERTAIN SETS OF ELEMENTS IN A FREE GROUP;84
18;Chapter 11. ON EQUIVALENT SETS OF ELEMENTS IN A FREE GROUP;94
19;Chapter 12. SIMPLICIAL SPACES, NUCLEI AND m-GROUPS;114
20;Chapter 13. ON CERTAIN INVARIANTS INTRODUCED BY REIDEMEISTER;200
21;Chapter 14. ON THE ASPHERICITY OF REGIONS IN A 3-SPHERE;204
22;Chapter 15. ON C1-COMPLEXES;222
23;Chapter 16. ON THE HOMOTOPY TYPE OF MANIFOLDS;238
23.1;NOTE ON MANIFOLDS;246
24;Chapter 17.ON ADDING RELATIONS TO HOMOTOPY GROUPS;250
24.1;ERRATA;269
25;Chapter 18. NOTE ON A PREVIOUS PAPER ENTITLED "ON ADDING RELATIONS TO HOMOTOPY GROUPS";270
26;Chapter 19. ON INCIDENCE MATRICES, NUCLEI AND HOMOTOPY TYPES;274
27;Chapter 20. ON THE GROUPS pr(Vn,m) AND SPHERE-BUNDLES;318
27.1;ERRATA;366
28;Chapter 21. ON THE GROUPS pr(Vn,m) AND SPHERE-BUNDLES (CORRIGENDUM);368
29;Chapter 22. VECTOR FIELDS ON THE n-SPHERE;372
30;Chapter 23. ON OPERATORS IN RELATIVE HOMOTOPY GROUPS;378
30.1;1. Introduction;378
30.2;2. The operators;379
30.3;3 .A multiplication in ., (.1,B);381
30.4;4. A family of groups contained in .1(A,B
);383
30.5;5. A group of automorphisms of pn(Q, P );385
30.6;6. Decomposition of He;385
30.7;7. Algebraic digression;390
30.8;8. A special case of p2(Q, P);396
30.9;9. A special case of .n{Q, P);402
30.10;10. Another special case;403
30.11;11. Proof of Lemma 1;406
30.12;12. Proof of Theorem 2;407
31;Chapter 24. NOTE ON SUSPENSION;410
31.1;1. Introduction;410
31.2;2. The crude suspension lemmas;411
31.3;3 . The crude suspension theorem;414
31.4;4. Application of Theorem 1;417
31.5;5 . A theorem on pm(Y);418
31.6;6. The delicate suspension theorems;421
31.7;7. Note on polyhedra;422
31.8;REFERENCES;423
32;Chapter 25. TEORIA DELLA DIMENSIONE;424
32.1;BIBLIOGRAFIA;431
33;Chapter 26. OMOTOPIA;432
33.1;BIBLIOGRAFIA;444
34;CONTENTS OF VOLUMES I TO IV;446