Quantum invariants and finite group actions on three-manifolds

Nafaa Chbili

doi:10.1016/S0166-8641(03)00221-9

Quantum invariants and finite group actions on three-manifolds

Nafaa Chbili

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

A 3-manifold M is said to be p-periodic (p≥2 an integer) if and only if the finite cyclic group of order p acts on M with a circle as the set of fixed points. This paper provides a criterion for periodicity of rational homology three-spheres. Namely, we give a necessary condition for a rational homology three-sphere to be periodic with a prime period. This condition is given in terms of the quantum SU(3) invariant. We also discuss similar results for the Murakami-Ohtsuki-Okada invariant.

Original language	English
Pages (from-to)	219-231
Number of pages	13
Journal	Topology and its Applications
Volume	136
Issue number	1-3
DOIs	https://doi.org/10.1016/S0166-8641(03)00221-9
Publication status	Published - Jan 28 2004
Externally published	Yes

Keywords

Group actions
Periodic links
Quantum invariants
Rational homology three-spheres

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.1016/S0166-8641(03)00221-9

Cite this

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title = "Quantum invariants and finite group actions on three-manifolds",

abstract = "A 3-manifold M is said to be p-periodic (p≥2 an integer) if and only if the finite cyclic group of order p acts on M with a circle as the set of fixed points. This paper provides a criterion for periodicity of rational homology three-spheres. Namely, we give a necessary condition for a rational homology three-sphere to be periodic with a prime period. This condition is given in terms of the quantum SU(3) invariant. We also discuss similar results for the Murakami-Ohtsuki-Okada invariant.",

keywords = "Group actions, Periodic links, Quantum invariants, Rational homology three-spheres",

author = "Nafaa Chbili",

note = "Funding Information: ✩ This work was partially completed during my stay at the Research Institute for Mathematical Sciences, Kyoto University, Japan. I would like to express my thanks and gratitude to the Mitsubishi Foundation and the Sumitomo Foundation for their financial support. I am also grateful to Hitoshi Murakami for his kind hospitality. E-mail address: [email protected] (N. Chbili).",

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T1 - Quantum invariants and finite group actions on three-manifolds

AU - Chbili, Nafaa

N1 - Funding Information: ✩ This work was partially completed during my stay at the Research Institute for Mathematical Sciences, Kyoto University, Japan. I would like to express my thanks and gratitude to the Mitsubishi Foundation and the Sumitomo Foundation for their financial support. I am also grateful to Hitoshi Murakami for his kind hospitality. E-mail address: [email protected] (N. Chbili).

PY - 2004/1/28

Y1 - 2004/1/28

N2 - A 3-manifold M is said to be p-periodic (p≥2 an integer) if and only if the finite cyclic group of order p acts on M with a circle as the set of fixed points. This paper provides a criterion for periodicity of rational homology three-spheres. Namely, we give a necessary condition for a rational homology three-sphere to be periodic with a prime period. This condition is given in terms of the quantum SU(3) invariant. We also discuss similar results for the Murakami-Ohtsuki-Okada invariant.

AB - A 3-manifold M is said to be p-periodic (p≥2 an integer) if and only if the finite cyclic group of order p acts on M with a circle as the set of fixed points. This paper provides a criterion for periodicity of rational homology three-spheres. Namely, we give a necessary condition for a rational homology three-sphere to be periodic with a prime period. This condition is given in terms of the quantum SU(3) invariant. We also discuss similar results for the Murakami-Ohtsuki-Okada invariant.

KW - Group actions

KW - Periodic links

KW - Quantum invariants

KW - Rational homology three-spheres

UR - https://www.scopus.com/pages/publications/0344514074

UR - https://www.scopus.com/pages/publications/0344514074#tab=citedBy

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DO - 10.1016/S0166-8641(03)00221-9

M3 - Article

AN - SCOPUS:0344514074

SN - 0166-8641

VL - 136

SP - 219

EP - 231

JO - Topology and its Applications

JF - Topology and its Applications

IS - 1-3

ER -

Quantum invariants and finite group actions on three-manifolds

Abstract

Keywords

ASJC Scopus subject areas

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