Author | Saeki, Osamu. author |
---|---|

Title | Topology of Singular Fibers of Differentiable Maps [electronic resource] / by Osamu Saeki |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 2004 |

Connect to | http://dx.doi.org/10.1007/b100393 |

Descript | X, 154 p. online resource |

SUMMARY

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

CONTENT

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

Mathematics
Manifolds (Mathematics)
Complex manifolds
Mathematics
Manifolds and Cell Complexes (incl. Diff.Topology)