© 2004

Topology of Singular Fibers of Differentiable Maps

  • Authors

Part of the Lecture Notes in Mathematics book series (LNM, volume 1854)

Table of contents

  1. Front Matter
    Pages N2-X
  2. Osamu Saeki
    Pages 1-5
  3. Osamu Saeki
    Pages 122-129
  4. Osamu Saeki
    Pages 131-134
  5. Osamu Saeki
    Pages 135-145
  6. Back Matter
    Pages 147-151

About this book


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.


Euler characteristics cobordism of singular maps manifold singular fiber staple map universal complex

About the authors

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.

Bibliographic information

  • Book Title Topology of Singular Fibers of Differentiable Maps
  • Authors Osamu Saeki
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title LNM
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-23021-2
  • eBook ISBN 978-3-540-44648-4
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages X, 154
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Manifolds and Cell Complexes (incl. Diff.Topology)
  • Buy this book on publisher's site


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." (Richárd Rimányi, Zentralblatt MATH, Vol. 1072, 2005)