Computing fundamental group of general 3-manifold

Junho Kim, Miao Jin, Qian Yi Zhou, Feng Luo, Xianfeng Gu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations


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.

Original languageEnglish (US)
Title of host publicationAdvances in Visual Computing - 4th International Symposium, ISVC 2008, Proceedings
Number of pages10
EditionPART 1
StatePublished - 2008
Event4th International Symposium on Visual Computing, ISVC 2008 - Las Vegas, NV, United States
Duration: Dec 1 2008Dec 3 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume5358 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other4th International Symposium on Visual Computing, ISVC 2008
Country/TerritoryUnited States
CityLas Vegas, NV

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


  • 3-manifold
  • CW-cell decomposition
  • Computational topology
  • Fundamental group


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