Computing fundamental group of general 3-manifold

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

doi:10.1007/978-3-540-89639-5_92

Computing fundamental group of general 3-manifold

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

School of Arts and Sciences, Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Scopus citations

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.

Original language	English (US)
Title of host publication	Advances in Visual Computing - 4th International Symposium, ISVC 2008, Proceedings
Pages	965-974
Number of pages	10
Edition	PART 1
DOIs	https://doi.org/10.1007/978-3-540-89639-5_92
State	Published - 2008
Event	4th International Symposium on Visual Computing, ISVC 2008 - Las Vegas, NV, United States Duration: Dec 1 2008 → Dec 3 2008

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Number	PART 1
Volume	5358 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	4th International Symposium on Visual Computing, ISVC 2008
Country/Territory	United States
City	Las Vegas, NV
Period	12/1/08 → 12/3/08

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Keywords

3-manifold
CW-cell decomposition
Computational topology
Fundamental group

Access to Document

10.1007/978-3-540-89639-5_92

Cite this

Kim, J., Jin, M., Zhou, Q. Y., Luo, F., & Gu, X. (2008). Computing fundamental group of general 3-manifold. In Advances in Visual Computing - 4th International Symposium, ISVC 2008, Proceedings (PART 1 ed., pp. 965-974). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5358 LNCS, No. PART 1). https://doi.org/10.1007/978-3-540-89639-5_92

@inproceedings{b0f179b0b4f440a7b69ec93175884f76,

title = "Computing fundamental group of general 3-manifold",

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.",

keywords = "3-manifold, CW-cell decomposition, Computational topology, Fundamental group",

author = "Junho Kim and Miao Jin and Zhou, {Qian Yi} and Feng Luo and Xianfeng Gu",

year = "2008",

doi = "10.1007/978-3-540-89639-5_92",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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booktitle = "Advances in Visual Computing - 4th International Symposium, ISVC 2008, Proceedings",

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note = "4th International Symposium on Visual Computing, ISVC 2008 ; Conference date: 01-12-2008 Through 03-12-2008",

}

Kim, J, Jin, M, Zhou, QY, Luo, F & Gu, X 2008, Computing fundamental group of general 3-manifold. in Advances in Visual Computing - 4th International Symposium, ISVC 2008, Proceedings. PART 1 edn, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 5358 LNCS, pp. 965-974, 4th International Symposium on Visual Computing, ISVC 2008, Las Vegas, NV, United States, 12/1/08. https://doi.org/10.1007/978-3-540-89639-5_92

Computing fundamental group of general 3-manifold. / Kim, Junho; Jin, Miao; Zhou, Qian Yi et al.

Advances in Visual Computing - 4th International Symposium, ISVC 2008, Proceedings. PART 1. ed. 2008. p. 965-974 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5358 LNCS, No. PART 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Computing fundamental group of general 3-manifold

AU - Kim, Junho

AU - Jin, Miao

AU - Zhou, Qian Yi

AU - Luo, Feng

AU - Gu, Xianfeng

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - 3-manifold

KW - CW-cell decomposition

KW - Computational topology

KW - Fundamental group

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SN - 9783540896388

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Kim J, Jin M, Zhou QY, Luo F, Gu X. Computing fundamental group of general 3-manifold. In Advances in Visual Computing - 4th International Symposium, ISVC 2008, Proceedings. PART 1 ed. 2008. p. 965-974. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1). doi: 10.1007/978-3-540-89639-5_92

Computing fundamental group of general 3-manifold

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All Science Journal Classification (ASJC) codes

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