Singularity Theory of Differentiable Maps and Data Visualization

  • Osamu Saeki
Part of the Mathematics for Industry book series (MFI, volume 5)


In many scientific situations, a given set of large data, obtained through simulation or experiment, can be considered to be a discrete set of sample values of a differentiable map between Euclidean spaces or between manifolds. From such a viewpoint, this article explores how the singularity theory of differentiable maps is useful in the visualization of such data. Special emphasis is put on Reeb graphs for scalar functions and on singular fibers of multi-variate functions.


Data visualization Multi-variate function Differential topology  Singularity theory Reeb graph Singular fiber 



Some of the contents of this article are the results of joint work with Professor Shigeo Takahashi (Graduate School of Frontier Sciences, the University of Tokyo), who kindly provided important materials for this article. The author would like to take this opportunity to express his sincere gratitude to him.


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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Institute of Mathematics for IndustryKyushu UniversityFukuokaJapan

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