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Computing Fundamental Group of General 3-Manifold

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Advances in Visual Computing (ISVC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5358))

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Abstract

Fundamental group is one of the most important topological invariants for general manifolds, which can be directly used as manifolds classification. In this work, we provide a series of practical and efficient algorithms to compute fundamental groups for general 3-manifolds based on CW cell decomposition. The input is a tetrahedral mesh, while the output is symbolic representation of its first fundamental group. We further simplify the fundamental group representation using computational algebraic method. We present the theoretical arguments of our algorithms, elaborate the algorithms with a number of examples, and give the analysis of their computational complexity.

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Author information

Authors and Affiliations

  1. Dong-Eui University, South Korea

    Junho Kim

  2. University of Louisiana at Lafayette, USA

    Miao Jin

  3. University of Southern California, USA

    Qian-Yi Zhou

  4. Rutgers University, USA

    Feng Luo

  5. Stony Brook University, USA

    Xianfeng Gu

Authors
  1. Junho Kim
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  2. Miao Jin
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  3. Qian-Yi Zhou
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  4. Feng Luo
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  5. Xianfeng Gu
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Nevada, Reno, USA

    George Bebis

  2. NASA Ames Research Center, Moffett Field, CA, USA

    Richard Boyle

  3. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Bahram Parvin

  4. Desert Research Institute, Reno, NV, USA

    Darko Koracin

  5. Digital Image Research Center, Kingston University, London, UK

    Paolo Remagnino

  6. Mitsubishi Electric Research Laboratories, P.O. Box 02139, Cambridge, MA, USA

    Fatih Porikli

  7. Computer and Information Science and Engineering, University of Florida, P.O. Box, FL 32611-6120, Gainsville, USA

    Jörg Peters

  8. IBM T.J. Watson Research Center, 19 Skyline Drive, NY 10532, Hawthorne, USA

    James Klosowski

  9. 128 Memorial Mall, Stewart B001, IN 47907, West Lafayette, USA

    Laura Arns

  10. Denver Museum of Nature and Space, 2001 Colorade Blvd. Denver,, CO 80205, USA

    Yu Ka Chun

  11. Departmen of Computer Science,, NC State University, Campus Box 8206, NC 27695-8206, Raleigh, USA

    Theresa-Marie Rhyne

  12. Los Alamos National Labs, P.O. Box 1663, NM 87545, Los Alamos, USA

    Laura Monroe

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© 2008 Springer-Verlag Berlin Heidelberg

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Kim, J., Jin, M., Zhou, QY., Luo, F., Gu, X. (2008). Computing Fundamental Group of General 3-Manifold. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2008. Lecture Notes in Computer Science, vol 5358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89639-5_92

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  • DOI: https://doi.org/10.1007/978-3-540-89639-5_92

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89638-8

  • Online ISBN: 978-3-540-89639-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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