Complexes and Manifolds : The Mathematical Works of J. H. C. Whitehead.

Front Cover -- Complexes and Manifolds -- Copyright Page -- Table of Contents -- EDITORIAL PREFACE -- ACKNOWLEDGMENT -- PUBLICATIONS OF J. H. C. WHITEHEAD -- Chapter 1. ON ANALYTICAL COMPLEXES -- Chapter 2. ON DUALITY AND INTERSECTION CHAINS IN COMBINATORIAL ANALYSIS SITUS -- Chapter 3. ON SUBDIVISIONS OF COMPLEXES -- Chapter 4. CERTAIN THEOREMS ABOUT THREE DIMENSIONAL MANIFOLDS (I) -- Chapter 5. THREE-DIMENSIONAL MANIFOLDS (CORRIGENDUM) -- Chapter 6. A CERTAIN REGION IN EUCLIDEAN 3-SPACE -- Chapter 7. A CERTAIN OPEN MANIFOLD WHOSE GROUP IS UNITY -- Chapter 8. ON THE GROUP OF A CERTAIN LINKAGE -- Chapter 9. ON DOUBLED KNOTS -- Chapter 10. ON CERTAIN SETS OF ELEMENTS IN A FREE GROUP -- Chapter 11. ON EQUIVALENT SETS OF ELEMENTS IN A FREE GROUP -- Chapter 12. SIMPLICIAL SPACES, NUCLEI AND m-GROUPS -- Chapter 13. ON CERTAIN INVARIANTS INTRODUCED BY REIDEMEISTER -- Chapter 14. ON THE ASPHERICITY OF REGIONS IN A 3-SPHERE -- Chapter 15. ON C1-COMPLEXES -- Chapter 16. ON THE HOMOTOPY TYPE OF MANIFOLDS -- NOTE ON MANIFOLDS -- Chapter 17.ON ADDING RELATIONS TO HOMOTOPY GROUPS -- ERRATA -- Chapter 18. NOTE ON A PREVIOUS PAPER ENTITLED "ON ADDING RELATIONS TO HOMOTOPY GROUPS -- Chapter 19. ON INCIDENCE MATRICES, NUCLEI AND HOMOTOPY TYPES -- Chapter 20. ON THE GROUPS πr(Vn,m) AND SPHERE-BUNDLES -- ERRATA -- Chapter 21. ON THE GROUPS πr(Vn,m) AND SPHERE-BUNDLES (CORRIGENDUM) -- Chapter 22. VECTOR FIELDS ON THE n-SPHERE -- Chapter 23. ON OPERATORS IN RELATIVE HOMOTOPY GROUPS -- 1. Introduction -- 2. The operators -- 3 .A multiplication in γ, (.1,B) -- 4. A family of groups contained in γ1(A,B ) -- 5. A group of automorphisms of πn(Q, P ) -- 6. Decomposition of He -- 7. Algebraic digression -- 8. A special case of π2(Q, P) -- 9. A special case of Πn{Q, P) -- 10. Another special case -- 11. Proof of Lemma 1 -- 12. Proof of Theorem 2.

Chapter 24. NOTE ON SUSPENSION -- 1. Introduction -- 2. The crude suspension lemmas -- 3 . The crude suspension theorem -- 4. Application of Theorem 1 -- 5 . A theorem on πm(Y) -- 6. The delicate suspension theorems -- 7. Note on polyhedra -- REFERENCES -- Chapter 25. TEORIA DELLA DIMENSIONE -- BIBLIOGRAFIA -- Chapter 26. OMOTOPIA -- BIBLIOGRAFIA -- CONTENTS OF VOLUMES I TO IV.

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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.