Topology of Singular Fibers of Differentiable Maps
Saeki, Osamu.
Topology of Singular Fibers of Differentiable Maps [electronic resource] / by Osamu Saeki. - X, 154 p. online resource. - Lecture Notes in Mathematics, 1854 0075-8434 ; . - Lecture Notes in Mathematics, 1854 .
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. 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.
9783540446484
10.1007/b100393 doi
Cell aggregation--Mathematics.
Manifolds and Cell Complexes (incl. Diff.Topology).
QA613-613.8 QA613.6-613.66
514.34
Topology of Singular Fibers of Differentiable Maps [electronic resource] / by Osamu Saeki. - X, 154 p. online resource. - Lecture Notes in Mathematics, 1854 0075-8434 ; . - Lecture Notes in Mathematics, 1854 .
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. 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.
9783540446484
10.1007/b100393 doi
Cell aggregation--Mathematics.
Manifolds and Cell Complexes (incl. Diff.Topology).
QA613-613.8 QA613.6-613.66
514.34