Topology of Singular Fibers of Differentiable Maps (Lecture Notes in Mathematics, 1854)

The Volume Develops A Thorough Theory Of Singular Fibers Of Generic Differentiable Maps. This Is The First Work That Establishes The Foundational Framework Of The Global Study Of Singular Differentiable Maps Of Negative Codimension From The Viewpoint Of Differential Topology. The Book Contains Not Only A General Theory, But Also Some Explicit Examples Together With A Number Of Very Concrete Applications. This Is A Very Interesting Subject In Differential Topology, Since It Shows A Beautiful Interplay Between The Usual Theory Of Singularities Of Differentiable Maps And The Geometric Topology Of Manifolds. Part I. Classification Of Singular Fibers: Preliminaries; Singular Fibers Of Morse Functions On Surfaces; Classification Of Singular Fibers; Co-existence Of Singular Fibers; Euler Characteristic Of The Source 4-manifold; Examples Of Stable Maps Of 4-manifolds -- Part Ii. Universal Complex Of Singular Fibers: Generalities; Universal Complex Of Singular Fibers; Stable Maps Of 4-manifolds Into 3-manifolds; Co-orientable Singular Fibers; Homomorphism Induced By A Thom Map; Cobordism Invariance; Cobordism Of Maps With Prescribed Local Singularities; Examples Of Cobordism Invariants -- Part Iii. Epilogue: Applications; Further Developments; References; List Of Symbols; Index. Osamu Saeki. Includes Bibliographical References (p. [131]-134) And Index. The volume develops a thorough theory of singular fibers of generic differentiable maps. This is the first work that establishes the foundational framework of the global study of singulardifferentiable maps of negative codimension from the viewpoint of differential topology. The book contains not only a general theory, but also some explicit examples together with a number of very concrete applications. This is a very interesting subject in differential topology, since it shows a beautiful interplay between the usual theory of singularities of differentiable maps and the geometric topology of manifolds. TOC:Part I. Classification of Singular Fibers: Preliminaries.- Singular Fibers of Morse Functions on Surfaces.- Classification of Singular Fibers.- Co-existence of Singular Fibers.- Euler Characteristic of the Source 4-Manifold.- Examples of Stable Maps of 4-Manifolds.- Part II. Universal Complex of Singular Fibers: Generalities.- Universal Complex of Singular Fibers.- Stable Maps of 4-Manifolds into 3-Manifolds.- Co-orientable Singular Fibers.- Homomorphism Induced by a Thom Map.-Cobordism Invariance.- Cobordism of Maps with Prescribed Local Singularities.- Examples of Cobordism Invariants.- Part III. Epilogue: Applications.- Further Developments.- References.- List of Symbols.- Index "The volume develops a thorough theory of singular fibers of generic differentiable maps. This is the first work that establishes the foundational framework of the global study of singular differentiable maps of negative codimension from the viewpoint of differential topology. The book contains not only a general theory, but also some explicit examples together with a number of very concrete applications."--BOOK JACKET Introduction....Pages 1-5 Part I: Classification of Singular Fibers....Pages 7-57 Part II: Universal Complex of Singular Fibers....Pages 59-120 Part III: Epilogue....Pages 121-129 References....Pages 131-134 List of Symbols and Index....Pages 135-145