Computing Fundamental Group of General 3-Manifold

Authors:
Junho Kim;Miao Jin;Qian-Yi Zhou;Feng Luo;Xianfeng Gu
Affiliations:
Dong-Eui University, South Korea;University of Louisiana at Lafayette, USA;University of Southern California, USA;Rutgers University, USA;Stony Brook University, USA
Venue:
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
Year:
2008

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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.