TY - JOUR
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: nafaa.chbili@esstt.rnu.tn (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 - http://www.scopus.com/inward/record.url?scp=0344514074&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0344514074&partnerID=8YFLogxK
U2 - 10.1016/S0166-8641(03)00221-9
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 -