Topology of Singular Fibers of Differentiable Maps

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.

• 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.

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)