Topology of Singular Fibers of Differentiable Maps

2004
ISBN: 978-3-540-23021-2
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1854, 154 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 260 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Saeki, Osamu

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Analytische Topologie

Inhaltsverzeichnis

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.

Über Autor(innen)

The author received his Ph.D. from the University of Tokyo in 1992. He has taught at Yamagata University, Hiroshima University, and is currently a Professor at Kyushu University, Japan.