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Topological Methods in Data Analysis and Visualization

TopoInVis 2015: Topological Methods in Data Analysis and Visualization IV pp 3–33Cite as

Theory of Singular Fibers and Reeb Spaces for Visualization

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Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

This is a survey article on singularity theory of differentiable maps with applications to visualization of scientific data in mind. Special emphasis is put on Morse theory on manifolds with boundary, singular fibers of multi-fields, their Reeb spaces, and their topological transitions.

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Acknowledgements

The author would like to express his sincere gratitude to Hamish Carr, Christoph Garth and Tino Weinkauf for organizing the TopoInVis 2015, and for inviting him for a keynote lecture. Special thanks are to Hamish Carr for his essential comments for an earlier version, which drastically improved the presentation of the article. He would also like to thank all the participants for exciting discussions after the talk. The author also would like to thank Shigeo Takahashi, Daisuke Sakurai, Masayuki Kawashima, Kazuto Takao and Amit Chattopadhyay for stimulating discussions and for posing interesting questions. Finally, the author would like to thank the anonymous reviewer for various comments which improved the presentation of the paper.

The author has been supported in part by JSPS KAKENHI Grant Numbers JP23244008, JP23654028, JP25540041, JP15K13438.

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Authors and Affiliations

  1. Institute of Mathematics for Industry, Kyushu University, Motooka 744, Nishi-ku, Fukuoka, 819-0395, Japan

    Osamu Saeki

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  1. Osamu Saeki
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Correspondence to Osamu Saeki .

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Editors and Affiliations

  1. University of Leeds, Leeds, United Kingdom

    Hamish Carr

  2. Department of Computer Science, Technical University of Kaiserslautern, Kaiserslautern, Germany

    Christoph Garth

  3. School of Computer Science and Communication, KTH Royal Institute of Technology, Stockholm, Sweden

    Tino Weinkauf

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Saeki, O. (2017). Theory of Singular Fibers and Reeb Spaces for Visualization. In: Carr, H., Garth, C., Weinkauf, T. (eds) Topological Methods in Data Analysis and Visualization IV. TopoInVis 2015. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-44684-4_1

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