Topology of Singular Fibers of Differentiable Maps

By: Osamu Saeki

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Paperback | 22 September 2004

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164 Pages

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23.39 x 15.6 x 0.89

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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.

Industry Reviews

From the reviews of the first edition:

"The book is a systematic summary of the author's research done in the past decade ... . The book is undoubtedly a milestone in global singularity theory of smooth maps of negative codimension: a very promising research topic. This clearly written and nicely illustrated volume is suitable for anybody in the field from graduate students to researchers." (Richard Rimanyi, Zentralblatt MATH, Vol. 1072, 2005)

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Preliminaries	p. 9
Singular fibers of Morse functions on surfaces	p. 13
Classification of singular fibers	p. 21
Co-existence of singular fibers	p. 39
Euler characteristic of the source 4-manifold	p. 43
Examples of stable maps of 4-manifolds	p. 47
Generalities	p. 61
Universal complex of singular fibers	p. 65
Stable maps of 4-manifolds into 3-manifolds	p. 83
Co-orientable singular fibers	p. 89
Homomorphism induced by a Thom map	p. 97
Cobordism invariance	p. 105
Cobordism of maps with prescribed local singularities	p. 113
Examples of cobordism invariants	p. 117
Applications	p. 123
Further developments	p. 127
Table of Contents provided by Blackwell. All Rights Reserved.

Topology of Singular Fibers of Differentiable Maps

At a Glance

Paperback

Industry Reviews

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